Biconformal deformations in the presence of a conformal foliation by curves are exploited to study equivalence between 3-dimensional Ricci solitons. We show that a wide class of solitons are biconformally equivalent to the flat metric.
{"title":"Biconformal equivalence between 3-dimensional Ricci solitons","authors":"P. Baird, Elsa Ghandour","doi":"10.2748/tmj.20200428","DOIUrl":"https://doi.org/10.2748/tmj.20200428","url":null,"abstract":"Biconformal deformations in the presence of a conformal foliation by curves are exploited to study equivalence between 3-dimensional Ricci solitons. We show that a wide class of solitons are biconformally equivalent to the flat metric.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47065741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-integrated defect relation for meromorphic maps from Kähler manifolds with hypersurfaces of a projective variety in subgeneral position","authors":"S. Quang, Lê Ngọc Quỳnh, N. Nhung","doi":"10.2748/tmj.20200219","DOIUrl":"https://doi.org/10.2748/tmj.20200219","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86426098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce entire multiple zeta functions, which are natural interpolations of symmetric multiple zeta values. Moreover we give further generalizations which interpolate these zeta functions, $widehat{mathcal{A}}$-finite multiple zeta values and $widehat{mathcal{S}}$-symmetric multiple zeta values. We also show that the correspondence which Kaneko--Zagier conjecture suggests holds on nonpositive integers for finite multiple zeta values and special values of these multiple zeta functions.
{"title":"Finite multiple zeta values, symmetric multiple zeta values and unified multiple zeta functions","authors":"Y. Komori","doi":"10.2748/tmj.20200226","DOIUrl":"https://doi.org/10.2748/tmj.20200226","url":null,"abstract":"We introduce entire multiple zeta functions, which are natural interpolations of symmetric multiple zeta values. Moreover we give further generalizations which interpolate these zeta functions, $widehat{mathcal{A}}$-finite multiple zeta values and $widehat{mathcal{S}}$-symmetric multiple zeta values. We also show that the correspondence which Kaneko--Zagier conjecture suggests holds on nonpositive integers for finite multiple zeta values and special values of these multiple zeta functions.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42937919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is known that the class of developable surfaces which have zero Gaussian curvature in three dimensional Euclidean space is preserved by the parallel transformations. A tangent developable surface is defined as a ruled developable surface by tangent lines to a space curve and it has singularities at least along the space curve, called the directrix or the the edge of regression. Also the class of tangent developable surfaces are invariant under the parallel deformations. In this paper the notions of tangent developable surfaces and their parallels are naturally generalized for frontal curves in general in Euclidean spaces of arbitrary dimensions. We study singularities appearing on parallels to tangent developable surfaces of frontal curves and give the classification of generic singularities on them for frontal curves in 3 or 4 dimensional Euclidean spaces.
{"title":"Singularities of parallels to tangent developable surfaces","authors":"G. Ishikawa","doi":"10.2748/tmj.20211220","DOIUrl":"https://doi.org/10.2748/tmj.20211220","url":null,"abstract":"It is known that the class of developable surfaces which have zero Gaussian curvature in three dimensional Euclidean space is preserved by the parallel transformations. A tangent developable surface is defined as a ruled developable surface by tangent lines to a space curve and it has singularities at least along the space curve, called the directrix or the the edge of regression. Also the class of tangent developable surfaces are invariant under the parallel deformations. In this paper the notions of tangent developable surfaces and their parallels are naturally generalized for frontal curves in general in Euclidean spaces of arbitrary dimensions. We study singularities appearing on parallels to tangent developable surfaces of frontal curves and give the classification of generic singularities on them for frontal curves in 3 or 4 dimensional Euclidean spaces.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49576341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Atsufumi Honda, K. Naokawa, K. Saji, M. Umehara, Kotaro Yamada
It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singular point. In this paper, we show a certain kind of uniqueness of such a coordinate system. In particular, the functions associated with this coordinate system produce new invariants on cross cap singular points. Using them, we classify the possible symmetries on cross caps.
{"title":"Symmetries of cross caps","authors":"Atsufumi Honda, K. Naokawa, K. Saji, M. Umehara, Kotaro Yamada","doi":"10.2748/tmj.20211203","DOIUrl":"https://doi.org/10.2748/tmj.20211203","url":null,"abstract":"It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singular point. In this paper, we show a certain kind of uniqueness of such a coordinate system. In particular, the functions associated with this coordinate system produce new invariants on cross cap singular points. Using them, we classify the possible symmetries on cross caps.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41849348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We compute Stokes matrices for generalised Airy equations and prove that they are regular unipotent (up to multiplication with the formal monodromy). This class of differential equations was defined by Katz and includes the classical Airy equation. In addition, it includes differential equations which are not rigid. Our approach is based on the topological computation of Stokes matrices of the enhanced Fourier-Sato transform of a perverse sheaf due to D'Agnolo, Hien, Morando and Sabbah.
{"title":"Stokes matrices for Airy equations","authors":"A. Hohl, Konstantin Jakob","doi":"10.2748/tmj.20210506","DOIUrl":"https://doi.org/10.2748/tmj.20210506","url":null,"abstract":"We compute Stokes matrices for generalised Airy equations and prove that they are regular unipotent (up to multiplication with the formal monodromy). This class of differential equations was defined by Katz and includes the classical Airy equation. In addition, it includes differential equations which are not rigid. Our approach is based on the topological computation of Stokes matrices of the enhanced Fourier-Sato transform of a perverse sheaf due to D'Agnolo, Hien, Morando and Sabbah.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41658843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global existence of small solutions for a quadratic nonlinear\u0000 fourth-order Schrödinger equation in six space dimensions","authors":"K. Aoki","doi":"10.2748/TMJ.20191217","DOIUrl":"https://doi.org/10.2748/TMJ.20191217","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"73 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42408772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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