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International Electronic Journal of Geometry最新文献

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Geometry of Twisted Products and Applications on Static Perfect Fluid Spacetimes 扭曲积的几何及其在静态完美流体时空上的应用
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1286525
Sinem GÜLER, U.c. DE, Bülent ÜNAL
{"title":"Geometry of Twisted Products and Applications on Static Perfect Fluid Spacetimes","authors":"Sinem GÜLER, U.c. DE, Bülent ÜNAL","doi":"10.36890/iejg.1286525","DOIUrl":"https://doi.org/10.36890/iejg.1286525","url":null,"abstract":"In this paper, first we study the harmonicity of the functions and forms on the twisted products, and then we determine its sectional curvature. We explore some characteristics of static perfect fluid and static vacuum spacetimes on twisted product manifolds by proving the existence and obstructions on Ricci curvature. Finally, we study the problem of the existence static perfect fluid spacetime associated with the twisted generalized Robertson-Walker and standard static spacetime metrics.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"59 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133635","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}
引用次数: 0
Characteristic Jacobi operator on almost Kenmotsu $3-manifolds 几乎Kenmotsu $3流形上的特征Jacobi算子
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1300339
Jun-ichi INOGUCHI
{"title":"Characteristic Jacobi operator on almost Kenmotsu $3-manifolds","authors":"Jun-ichi INOGUCHI","doi":"10.36890/iejg.1300339","DOIUrl":"https://doi.org/10.36890/iejg.1300339","url":null,"abstract":"The Ricci tensor field, $varphi$-Ricci tensor field and the characteristic Jacobi operator on almost Kenmotsu $3$-manifolds are investigated. We give a classification of locally symmetric almost Kenmotsu $3$-manifolds.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136134465","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}
引用次数: 0
On Statistical Submanifolds in Statistical Manifolds of Quasi-Constant Curvature 拟常曲率统计流形中的统计子流形
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1237417
Hülya AYTİMUR
{"title":"On Statistical Submanifolds in Statistical Manifolds of Quasi-Constant Curvature","authors":"Hülya AYTİMUR","doi":"10.36890/iejg.1237417","DOIUrl":"https://doi.org/10.36890/iejg.1237417","url":null,"abstract":"We mention some properties of statistical submanifolds in statistical manifolds of quasi-constant curvature. We obtain Chen first inequality and a Chen inequality for the $delta (2,2)$-invariant for these manifolds.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136134486","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}
引用次数: 0
A New Insight on Rectifying-Type Curves in Four-Dimensional Euclidean Space 四维欧几里德空间中校正型曲线的新认识
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1291893
Zehra İŞBİLİR, Murat TOSUN
{"title":"A New Insight on Rectifying-Type Curves in Four-Dimensional Euclidean Space","authors":"Zehra İŞBİLİR, Murat TOSUN","doi":"10.36890/iejg.1291893","DOIUrl":"https://doi.org/10.36890/iejg.1291893","url":null,"abstract":"In this study, our purpose is to determine the generalized rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$. Also, some characterizations of them are given. We construct some correlations between curvatures and invariants of generalized rectifying-type curves. Additionally, we obtain an illustrative example with respect to the rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133749","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}
引用次数: 1
Fuzzy Counterpart of Klein Quadric Klein二次函数的模糊对应物
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1343784
Ziya AKÇA, Abdilkadir ALTINTAŞ
{"title":"Fuzzy Counterpart of Klein Quadric","authors":"Ziya AKÇA, Abdilkadir ALTINTAŞ","doi":"10.36890/iejg.1343784","DOIUrl":"https://doi.org/10.36890/iejg.1343784","url":null,"abstract":"Many techniques have been proposed to project the high-dimensional space into a low-dimensional space, one of the most famous methods being principal component analysis. The Klein quadric is a geometric shape defined by a second-degree homogeneous equation. The lines of projective three-space are, via the Klein mapping, in one-to-one correspondence with points of a hyperbolic quadric of the projective 5-space. This paper presents a research study on he images under the Klein mapping of the projectice 3-space order of 4 and the fuzzification of the Klein quadric in 5-dimensional projective space.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"51 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133511","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}
引用次数: 0
COTTON SOLITONS ON THREE DIMENSIONAL ALMOST ALPHA-PARACOSYMPLECTIC MANIFOLDS 三维几乎副辛流形上的棉花孤子
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1316716
İrem KÜPELİ ERKEN, Mustafa ÖZKAN, Büşra SAVUR
{"title":"COTTON SOLITONS ON THREE DIMENSIONAL ALMOST ALPHA-PARACOSYMPLECTIC MANIFOLDS","authors":"İrem KÜPELİ ERKEN, Mustafa ÖZKAN, Büşra SAVUR","doi":"10.36890/iejg.1316716","DOIUrl":"https://doi.org/10.36890/iejg.1316716","url":null,"abstract":"In this paper, we study Cotton solitons on three-dimensional almost α-paracosymplectic manifolds. We especially focus on threedimensional almost α-paracosymplectic manifolds with harmonic vector field ξ and characterize them for all possible types of operator h. Finally, we constructed an example which satisfies our results.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133745","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}
引用次数: 1
Locally Product-like Statistical Manifolds and Their Hypersurfaces 局部类积统计流形及其超曲面
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1307467
Esra ERKAN, Kazuhiko TAKANO, Mehmet GÜLBAHAR
{"title":"Locally Product-like Statistical Manifolds and Their Hypersurfaces","authors":"Esra ERKAN, Kazuhiko TAKANO, Mehmet GÜLBAHAR","doi":"10.36890/iejg.1307467","DOIUrl":"https://doi.org/10.36890/iejg.1307467","url":null,"abstract":"In this paper, almost product-like Riemannian manifolds are investigated. Basic properties on tangential hypersurfaces of almost product-like Riemannian manifolds are obtained. Some examples of tangential hypersurfaces are presented. Some relations involving the Riemannian curvature tensor of a tangential hypersurface are computed.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"46 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133499","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}
引用次数: 2
Approximations of Parallel Surfaces Along Curves 沿曲线平行曲面的近似
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1362590
Büşra KÖSE, Yusuf YAYLI
{"title":"Approximations of Parallel Surfaces Along Curves","authors":"Büşra KÖSE, Yusuf YAYLI","doi":"10.36890/iejg.1362590","DOIUrl":"https://doi.org/10.36890/iejg.1362590","url":null,"abstract":"In this paper, we study developable surfaces which are flat and normal approximation of parallel surfaces along curves associated with three special vector fields. It is known that a surface whose points are at a constant distance along the normal of the surface is called a parallel surface. We investigate singularities of such developable surfaces. We show that under what conditions the approach surfaces are parallel. Also, we show that the approach surfaces are constant angle ruled surfaces if the curves selected on the surfaces are isophote, relatively normal-slant helix and helix.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"70 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133578","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}
引用次数: 0
Inextensible flows of space curves according to a new orthogonal frame with curvature in E_1^3 曲率为E_1^3的新正交坐标系下空间曲线的不可扩展流
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1274663
Alperen KIZILAY, Atakan Tuğkan YAKUT
{"title":"Inextensible flows of space curves according to a new orthogonal frame with curvature in E_1^3","authors":"Alperen KIZILAY, Atakan Tuğkan YAKUT","doi":"10.36890/iejg.1274663","DOIUrl":"https://doi.org/10.36890/iejg.1274663","url":null,"abstract":"Using a new orthogonal frame with curvature in $E_1^3$ and we put forth a new general formulation for inextensible flows of space curves in this work. We demonstrate presufficient conditions and prove the necessary conditions for inextensible curve flow which is a partial differential equations (PDE) incorporating the curvatures and torsion.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"59 19","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133633","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}
引用次数: 0
On a Sequence of Slant Submanifolds in Almost Product Riemannian Setting 关于几乎积黎曼集合中的一个倾斜子流形序列
International Electronic Journal of Geometry Pub Date : 2023-10-29 DOI: 10.36890/iejg.1321401
Adara M. BLAGA
{"title":"On a Sequence of Slant Submanifolds in Almost Product Riemannian Setting","authors":"Adara M. BLAGA","doi":"10.36890/iejg.1321401","DOIUrl":"https://doi.org/10.36890/iejg.1321401","url":null,"abstract":"We prove that the property of being pointwise slant is transitive on a class of proper pointwise slant submanifolds of almost product Riemannian manifolds, and illustrate this fact with an example. For a given almost product Riemannian manifold $(M_1,g,varphi_1)$, we consider a sequence of pointwise slant submanifolds $(M_{i+1}hookrightarrow M_i)_{iin mathbb{N}^*}$, and we explicitly determine the relation between the slant functions. Moreover, we state this result in a more general case.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":"59 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133634","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}
引用次数: 0
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