Pub Date : 2022-12-06DOI: 10.15673/tmgc.v15i3-4.2328
Abdessami Jalled, F. Haggui
The purpose of this paper is to study holomorphic curves f from C to C3 avoiding four complex hyperplanes and a real subspace of real dimension four in C3. We show that the projection of f into the complex projective space C P^2 does not remain constant as in the complex case studied by Green, which indicates that the complex structure of the avoided hyperplanes is a necessary condition in the Green theorem
{"title":"Some remarks on a theorem of Green","authors":"Abdessami Jalled, F. Haggui","doi":"10.15673/tmgc.v15i3-4.2328","DOIUrl":"https://doi.org/10.15673/tmgc.v15i3-4.2328","url":null,"abstract":"The purpose of this paper is to study holomorphic curves f from C to C3 avoiding four complex hyperplanes and a real subspace of real dimension four in C3. We show that the projection of f into the complex projective space C P^2 does not remain constant as in the complex case studied by Green, which indicates that the complex structure of the avoided hyperplanes is a necessary condition in the Green theorem","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73449970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.15673/tmgc.v15i3-4.2329
I. Kurbatova, M. Pistruil
The present paper continues the study of quasi-geodesic mappings f:(Vn, gij, Fih) → (V'n,g'ij, Fih) of pseudo-Riemannian spaces Vn, V'n with a generalized-recurrent structure Fih of parabolic type. By a generalized recurrent structure of parabolic type on Vn we mean an almost Hermitian affinor structure of parabolic type for which the covariant derivative of the structural affinor Fih satisfies the condition F(i,j)h=q(i Fj)h. In the previous paper by the authors [Proc. Intern. Geom. Center, 13:3 (2020) 18-32] it was proved that the class of pseudo-Riemannian spaces with generalized-recurrent structure of parabolic type is closed with respect to the considered mappings and the generalized recurrence vectors in (Vn, gij,Fih) and (V'_n, g'ij, Fih) may be distinct. In this article, it is assumed that the mapping f preserves the generalized recurrence vector qi. We construct geometric objects that are invariant under the quasi-geodesic mapping of generalized-recurrent spaces of parabolic type and recurrent-parabolic spaces. A number of conditions are given on these objects, which lead to the fact that a generalized-recurrent space of parabolic type admits a parabolic K-structure, and a recurrent-parabolic space admits a Kählerian structure of parabolic type. We study special types of these mappings that preserve some tensors of an intrinsic nature.
{"title":"Canonical quasi-geodesic mappings of special pseudo-Riemannian spaces","authors":"I. Kurbatova, M. Pistruil","doi":"10.15673/tmgc.v15i3-4.2329","DOIUrl":"https://doi.org/10.15673/tmgc.v15i3-4.2329","url":null,"abstract":"The present paper continues the study of quasi-geodesic mappings f:(Vn, gij, Fih) → (V'n,g'ij, Fih) of pseudo-Riemannian spaces Vn, V'n with a generalized-recurrent structure Fih of parabolic type. By a generalized recurrent structure of parabolic type on Vn we mean an almost Hermitian affinor structure of parabolic type for which the covariant derivative of the structural affinor Fih satisfies the condition F(i,j)h=q(i Fj)h. \u0000In the previous paper by the authors [Proc. Intern. Geom. Center, 13:3 (2020) 18-32] it was proved that the class of pseudo-Riemannian spaces with generalized-recurrent structure of parabolic type is closed with respect to the considered mappings and the generalized recurrence vectors in (Vn, gij,Fih) and (V'_n, g'ij, Fih) may be distinct. In this article, it is assumed that the mapping f preserves the generalized recurrence vector qi. \u0000We construct geometric objects that are invariant under the quasi-geodesic mapping of generalized-recurrent spaces of parabolic type and recurrent-parabolic spaces. A number of conditions are given on these objects, which lead to the fact that a generalized-recurrent space of parabolic type admits a parabolic K-structure, and a recurrent-parabolic space admits a Kählerian structure of parabolic type. \u0000We study special types of these mappings that preserve some tensors of an intrinsic nature.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83223237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-15DOI: 10.15673/tmgc.v15i2.2296
M. Pahirya, Yuliya Mislo
Інтерполяційний ланцюговий дріб Тіле з кратними вузлами є аналогом інтерполяційного многочлена Ерміта в теорії ланцюгових дробів. В роботі досліджується задача побудови оскуляторного (дотичного) до функції f в точці z0 інтерполяційного ланцюгового дробу Тіле (ОІЛДТ). Для обчислення коефіцієнтів OICFT використовуються лише значення функції f та її похідних у точці z0. Запропонований метод знаходження коефіцієнтів ґрунтується на обчислені значень m-кратних сум і не передбачає обчислення значень ганкелевих визначників.
{"title":"Оскуляторний інтерполяційний ланцюговий дріб Тіле","authors":"M. Pahirya, Yuliya Mislo","doi":"10.15673/tmgc.v15i2.2296","DOIUrl":"https://doi.org/10.15673/tmgc.v15i2.2296","url":null,"abstract":"Інтерполяційний ланцюговий дріб Тіле з кратними вузлами є аналогом інтерполяційного многочлена Ерміта в теорії ланцюгових дробів. В роботі досліджується задача побудови оскуляторного (дотичного) до функції f в точці z0 інтерполяційного ланцюгового дробу Тіле (ОІЛДТ). Для обчислення коефіцієнтів OICFT використовуються лише значення функції f та її похідних у точці z0. Запропонований метод знаходження коефіцієнтів ґрунтується на обчислені значень m-кратних сум і не передбачає обчислення значень ганкелевих визначників.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84622572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-03DOI: 10.15673/tmgc.v15i2.2226
I. Kurbatova, M. Pistruil
The present paper continues the study of quasi-geodesic mappings f:(Vn, gij, Fih) → (V'n,g'ij, Fih) of pseudo-Riemannian spaces Vn, V'n with a generalized-recurrent structure Fih of parabolic type. By a generalized recurrent structure of parabolic type on Vn we mean an almost Hermitian affinor structure of parabolic type for which the covariant derivative of the structural affinor Fih satisfies the condition F(i,j)h=q(i Fj)h. In the previous paper by the authors [Proc. Intern. Geom. Center, 13:3 (2020) 18-32] it was proved that the class of pseudo-Riemannian spaces with generalized-recurrent structure of parabolic type is closed with respect to the considered mappings and the generalized recurrence vectors in (Vn, gij,Fih) and (V'_n, g'ij, Fih) may be distinct. In this article, it is assumed that the mapping f preserves the generalized recurrence vector qi. We construct geometric objects that are invariant under the quasi-geodesic mapping of generalized-recurrent spaces of parabolic type and recurrent-parabolic spaces. A number of conditions are given on these objects, which lead to the fact that a generalized-recurrent space of parabolic type admits a parabolic K-structure, and a recurrent-parabolic space admits a Kählerian structure of parabolic type. We study special types of these mappings that preserve some tensors of an intrinsic nature.
{"title":"On quasi-geodesic mappings of special pseudo-Riemannian spaces","authors":"I. Kurbatova, M. Pistruil","doi":"10.15673/tmgc.v15i2.2226","DOIUrl":"https://doi.org/10.15673/tmgc.v15i2.2226","url":null,"abstract":"The present paper continues the study of quasi-geodesic mappings f:(Vn, gij, Fih) → (V'n,g'ij, Fih) of pseudo-Riemannian spaces Vn, V'n with a generalized-recurrent structure Fih of parabolic type. By a generalized recurrent structure of parabolic type on Vn we mean an almost Hermitian affinor structure of parabolic type for which the covariant derivative of the structural affinor Fih satisfies the condition F(i,j)h=q(i Fj)h. \u0000In the previous paper by the authors [Proc. Intern. Geom. Center, 13:3 (2020) 18-32] it was proved that the class of pseudo-Riemannian spaces with generalized-recurrent structure of parabolic type is closed with respect to the considered mappings and the generalized recurrence vectors in (Vn, gij,Fih) and (V'_n, g'ij, Fih) may be distinct. In this article, it is assumed that the mapping f preserves the generalized recurrence vector qi. \u0000We construct geometric objects that are invariant under the quasi-geodesic mapping of generalized-recurrent spaces of parabolic type and recurrent-parabolic spaces. A number of conditions are given on these objects, which lead to the fact that a generalized-recurrent space of parabolic type admits a parabolic K-structure, and a recurrent-parabolic space admits a Kählerian structure of parabolic type. \u0000We study special types of these mappings that preserve some tensors of an intrinsic nature.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"157 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86339705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-30DOI: 10.15673/tmgc.v15i2.2224
V. Kiosak, L. Kusik, V. Isaiev
We introduced special pseudo-Riemannian spaces, called geodesic A-symmetric spaces, into consideration. It is proven that there are no geodesic symmetric spaces and no geodesic Ricci symmetric spaces, which differ from spaces of constant curvature and Einstein spaces respectively. The research is carried out locally, by tensor methods, without any limitations imposed on a metric and a sign.
{"title":"Geodesic Ricci-symmetric pseudo-Riemannian spaces","authors":"V. Kiosak, L. Kusik, V. Isaiev","doi":"10.15673/tmgc.v15i2.2224","DOIUrl":"https://doi.org/10.15673/tmgc.v15i2.2224","url":null,"abstract":"We introduced special pseudo-Riemannian spaces, called geodesic A-symmetric spaces, into consideration. It is proven that there are no geodesic symmetric spaces and no geodesic Ricci symmetric spaces, which differ from spaces of constant curvature and Einstein spaces respectively. The research is carried out locally, by tensor methods, without any limitations imposed on a metric and a sign.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90881694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-18DOI: 10.15673/tmgc.v15i2.2281
M. Crasmareanu
We introduce and study a new frame and a new curvature function for a fixed parametrization of a spacelike curve in the Lorentz plane. This new frame is called flow-frame since it involves the time-dependent rotation of the usual Frenet flow.
{"title":"The flow-curvature of spacelike parametrized curves in the Lorentz plane","authors":"M. Crasmareanu","doi":"10.15673/tmgc.v15i2.2281","DOIUrl":"https://doi.org/10.15673/tmgc.v15i2.2281","url":null,"abstract":"We introduce and study a new frame and a new curvature function for a fixed parametrization of a spacelike curve in the Lorentz plane. This new frame is called flow-frame since it involves the time-dependent rotation of the usual Frenet flow.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"2002 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88318825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-10DOI: 10.15673/tmgc.v15i2.2020
A. Zaitov, K. Kurbanov
In the present paper proved that if for a given compact Hausdorff space X the hyperspace exp(X) is a contractible compact space then the space OSf(X) is also a contractible compact space. As a consequence it is established that the space OSf(X) of semi-additive functionals is absolute (neighbourhood) retract if and only if the hyperspace exp(X) is so.
{"title":"When is the space of semi-additive functionals an absolute (neighbourhood) retract?","authors":"A. Zaitov, K. Kurbanov","doi":"10.15673/tmgc.v15i2.2020","DOIUrl":"https://doi.org/10.15673/tmgc.v15i2.2020","url":null,"abstract":"In the present paper proved that if for a given compact Hausdorff space X the hyperspace exp(X) is a contractible compact space then the space OSf(X) is also a contractible compact space. As a consequence it is established that the space OSf(X) of semi-additive functionals is absolute (neighbourhood) retract if and only if the hyperspace exp(X) is so.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73643675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-20DOI: 10.15673/tmgc.v15i3-4.2338
A. Prishlyak, M. Loseva
We investigate the topological structure of flows on the Girl's surface which is one of two possible immersions of the projective plane in three-dimensional space with one triple point of self-intersection. First, we describe the cellular structure of the Boy's and Girl's surfaces and prove that there are unique images of the project plane in the form of a $2$-disk, in which the opposite points of the boundary are identified and this boundary belongs to the preimage of the $1$-skeleton of the surface. Second, we describe three structures of flows with one fixed point and no separatrices on the Girl's surface and prove that there are no other such flows. Third, we prove that Morse-Smale flows and they alone are structurally stable on the Boy's and Girl's surfaces. Fourth, we find all possible structures of optimal Morse-Smale flows on the Girl's surface. Fifth, we obtain a classification of Morse-Smale flows on the projective plane immersed on the Girl's surface. And finally, we describe the isotopic classes of these flows.
{"title":"Topological structure of optimal flows on the Girl's surface","authors":"A. Prishlyak, M. Loseva","doi":"10.15673/tmgc.v15i3-4.2338","DOIUrl":"https://doi.org/10.15673/tmgc.v15i3-4.2338","url":null,"abstract":"We investigate the topological structure of flows on the Girl's surface which is one of two possible immersions of the projective plane in three-dimensional space with one triple point of self-intersection. First, we describe the cellular structure of the Boy's and Girl's surfaces and prove that there are unique images of the project plane in the form of a $2$-disk, in which the opposite points of the boundary are identified and this boundary belongs to the preimage of the $1$-skeleton of the surface. Second, we describe three structures of flows with one fixed point and no separatrices on the Girl's surface and prove that there are no other such flows. Third, we prove that Morse-Smale flows and they alone are structurally stable on the Boy's and Girl's surfaces. Fourth, we find all possible structures of optimal Morse-Smale flows on the Girl's surface. Fifth, we obtain a classification of Morse-Smale flows on the projective plane immersed on the Girl's surface. And finally, we describe the isotopic classes of these flows.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90510262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-29DOI: 10.15673/tmgc.v15i3-4.2369
Jialong Deng
In an attempt to develop higher-dimensional quasiconformal mappings on metric measure spaces with curvature conditions, i.e. from Ahlfors to Alexandrov, we show that for n≥2 a noncollapsed RCD(0,n) space with Euclidean volume growth is an n-Loewner space and satisfies the infinitesimal-to-global principle.
{"title":"Quasiconformal mappings and curvatures on metric measure spaces","authors":"Jialong Deng","doi":"10.15673/tmgc.v15i3-4.2369","DOIUrl":"https://doi.org/10.15673/tmgc.v15i3-4.2369","url":null,"abstract":"In an attempt to develop higher-dimensional quasiconformal mappings on metric measure spaces with curvature conditions, i.e. from Ahlfors to Alexandrov, we show that for n≥2 a noncollapsed RCD(0,n) space with Euclidean volume growth is an n-Loewner space and satisfies the infinitesimal-to-global principle.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75605830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-28DOI: 10.15673/pigc.v16i2.2298
Jean-Pierre Magnot
We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give results on diffeological principal bundles with (a priori) no local trivialization including an Ambrose-Singer theorem, use the smoothing connections alrealy exhibited by the author in previous works, and finish with open questions.
{"title":"On diffeological principal bundles of non-formal pseudo-differential operators over formal ones","authors":"Jean-Pierre Magnot","doi":"10.15673/pigc.v16i2.2298","DOIUrl":"https://doi.org/10.15673/pigc.v16i2.2298","url":null,"abstract":"We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give results on diffeological principal bundles with (a priori) no local trivialization including an Ambrose-Singer theorem, use the smoothing connections alrealy exhibited by the author in previous works, and finish with open questions.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84738522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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