Abdulqader Mustafa, C. Ozel, A. Pigazzini, R. Pinčák
This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both known and new results. Moreover, a discrete example of contact $CR$-warped product submanifold in Kenmotsu manifold is constructed. For further research direction, we addressed a couple of open problems arose from the results of this paper.
{"title":"Existence and Nonexistence of Warped Product Submanifolds of Almost Contact Manifolds","authors":"Abdulqader Mustafa, C. Ozel, A. Pigazzini, R. Pinčák","doi":"10.36890/iejg.1131334","DOIUrl":"https://doi.org/10.36890/iejg.1131334","url":null,"abstract":"This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both known and new results. Moreover, a discrete example of contact $CR$-warped product submanifold in Kenmotsu manifold is constructed. For further research direction, we addressed a couple of open problems arose from the results of this paper.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44378488","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}
Let ( M n , g ) be a Riemannian manifold and TM n the total space of its tangent bundle. In this paper, we determine the infinitesimal fiber-preserving holomorphically projective (IFHP) transformations on TM n with respect to the Levi-Civita connection of the deformed complete lift metric ˜ G f = g C + ( fg ) V , where f is a nonzero differentiable function on M n and g C and g V are the complete lift and the vertical lift of g on TM n , respectively. Morevore, we prove that every IFHP transformation on ( TM n , ˜ G f ) is reduced to an affine and induces an infinitesimal affine transformation on ( M n , g ) .
{"title":"IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric","authors":"M. Zohrehvand","doi":"10.36890/iejg.1037651","DOIUrl":"https://doi.org/10.36890/iejg.1037651","url":null,"abstract":"Let ( M n , g ) be a Riemannian manifold and TM n the total space of its tangent bundle. In this paper, we determine the infinitesimal fiber-preserving holomorphically projective (IFHP) transformations on TM n with respect to the Levi-Civita connection of the deformed complete lift metric ˜ G f = g C + ( fg ) V , where f is a nonzero differentiable function on M n and g C and g V are the complete lift and the vertical lift of g on TM n , respectively. Morevore, we prove that every IFHP transformation on ( TM n , ˜ G f ) is reduced to an affine and induces an infinitesimal affine transformation on ( M n , g ) .","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49065677","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}
{"title":"Family of Surfaces","authors":"S. Şenyurt, K. H. Ayvaci, Davut Canlı","doi":"10.36890/iejg.932757","DOIUrl":"https://doi.org/10.36890/iejg.932757","url":null,"abstract":"","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41868592","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}
In this article, we present some results concerning the harmonicity on the tangent bundle equipped with the vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic with respect to the vertical rescaled metric and we construct some examples of harmonic vector fields. We also study the harmonicity of a vector field along with a map between Riemannian manifolds, the target manifold is equipped with a vertical rescaled metric on its tangent bundle. Next we also discuss the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being whose tangent bundle is endowed with a vertical rescaled metric. Finally, we study the harmonicity of the tangent map also the harmonicity of the identity map of the tangent bundle.
{"title":"Notes About a harmonicity on the tangent bundle with vertical rescaled metric","authors":"A. Zagane, N. Djaa","doi":"10.36890/iejg.1033998","DOIUrl":"https://doi.org/10.36890/iejg.1033998","url":null,"abstract":"In this article, we present some results concerning the harmonicity on the tangent bundle equipped with the vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic with respect to the vertical rescaled metric and we construct some examples of harmonic vector fields. We also study the harmonicity of a vector field along with a map between Riemannian manifolds, the target manifold is equipped with a vertical rescaled metric on its tangent bundle. Next we also discuss the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being whose tangent bundle is endowed with a vertical rescaled metric. Finally, we study the harmonicity of the tangent map also the harmonicity of the identity map of the tangent bundle.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47027648","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}
{"title":"Quasi Bi-Slant Submanifolds of Kaehler Manifolds","authors":"R. Prasad, M. Akyol, S. Verma, Sumeet Kumar","doi":"10.36890/iejg.1061786","DOIUrl":"https://doi.org/10.36890/iejg.1061786","url":null,"abstract":"","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48993248","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}
Ferdağ Kahraman Aksoyak, Burcu Bektaş Demirci, Murat Babaarslan
In this paper, we study on the characterizations of loxodromes on the rotational surfaces satisfying some special geometric properties such as having constant Gaussian curvature and a constant ratio of principal curvatures (CRPC rotational surfaces). First, we give the parametrizations of loxodromes parametrized by arc-length parameter on any rotational surfaces in $mathbb{E}^{3}$ and then, we calculate the curvature and the torsion of such loxodromes. Then, we give the parametrizations of loxodromes on rotational surfaces with constant Gaussian curvature. Also, we investigate the loxodromes on the CRPC rotational surfaces. Moreover, we give the parametrizations of loxodromes on the minimal rotational surface which is a special case of CRPC rotational surfaces. Finally, we give some visual examples to strengthen our main results via Wolfram Mathematica.
{"title":"Characterizations of Loxodromes on Rotational Surfaces in Euclidean 3-Space","authors":"Ferdağ Kahraman Aksoyak, Burcu Bektaş Demirci, Murat Babaarslan","doi":"10.36890/iejg.1161830","DOIUrl":"https://doi.org/10.36890/iejg.1161830","url":null,"abstract":"In this paper, we study on the characterizations of loxodromes on the rotational surfaces satisfying some special geometric properties such as having constant Gaussian curvature and a constant ratio of principal curvatures (CRPC rotational surfaces). \u0000First, we give the parametrizations of loxodromes parametrized by arc-length parameter on any rotational surfaces in $mathbb{E}^{3}$ \u0000and then, we calculate the curvature and the torsion of such loxodromes. \u0000Then, we give the parametrizations of loxodromes on rotational surfaces with constant Gaussian curvature. \u0000Also, we investigate the loxodromes on the CRPC rotational surfaces. \u0000Moreover, we give the parametrizations of loxodromes on the minimal rotational surface which is a special case of CRPC rotational surfaces. \u0000Finally, we give some visual examples to strengthen our main results via Wolfram Mathematica.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48962636","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}
{"title":"Special Mean and Total Curvature of a Dual Surface in Isotropic Spaces","authors":"A. Artykbaev, Sherzodbek Ismoi̇lov","doi":"10.36890/iejg.972370","DOIUrl":"https://doi.org/10.36890/iejg.972370","url":null,"abstract":"","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42979268","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}
{"title":"Finslerian viewpoint to the rectifying, normal, and osculating curves","authors":"Z. Ozdemir, Fatma Ateş, N. Ekmekci","doi":"10.36890/iejg.993188","DOIUrl":"https://doi.org/10.36890/iejg.993188","url":null,"abstract":"","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42906358","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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