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International Electronic Journal of Geometry最新文献

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Reversion Porisms in Conics 经济学中的回归现象
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-08-04 DOI: 10.36890/iejg.979088
L. Halbeisen, N. Hungerbuhler, M. Schiltknecht
{"title":"Reversion Porisms in Conics","authors":"L. Halbeisen, N. Hungerbuhler, M. Schiltknecht","doi":"10.36890/iejg.979088","DOIUrl":"https://doi.org/10.36890/iejg.979088","url":null,"abstract":"We give a projective proof of the butterfly porism for cyclic quadrilaterals and present a general reversion porism for polygons with an arbitrary number of vertices on a conic. We also investigate projective properties of the porisms.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44328896","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
Restricted Jacobi Fields 受限Jacobi域
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-07-25 DOI: 10.36890/iejg.945800
C. C. Remsing
{"title":"Restricted Jacobi Fields","authors":"C. C. Remsing","doi":"10.36890/iejg.945800","DOIUrl":"https://doi.org/10.36890/iejg.945800","url":null,"abstract":"We generalize the concept of a Jacobi field to nonholonomic Riemannian geometry, considering both nonholonomic Jacobi fields, and, more generally, restricted Jacobi fields. In the first case, the corresponding Jacobi equation involves the nonholonomic connection and the Schouten curvature tensor. In the second case, the Jacobi equation involves connections and curvature tensors arising in the construction of the Wagner curvature tensor. We also briefly discuss the existence of restricted Jacobi fields.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43111336","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
Framed Curves and Their Applications Based on a New Differential Equation 基于一种新的微分方程的框架曲线及其应用
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-07-02 DOI: 10.36890/iejg.875477
Bahar Doğan Yazıcı, Sıddıka ÖZKALDI KARAKUŞ, M. Tosun
{"title":"Framed Curves and Their Applications Based on a New Differential Equation","authors":"Bahar Doğan Yazıcı, Sıddıka ÖZKALDI KARAKUŞ, M. Tosun","doi":"10.36890/iejg.875477","DOIUrl":"https://doi.org/10.36890/iejg.875477","url":null,"abstract":"","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42159182","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
A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds 三维黎曼流形中梯度孤子的注记
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-04-15 DOI: 10.36890/IEJG.831078
F. Mofarreh
{"title":"A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds","authors":"F. Mofarreh","doi":"10.36890/IEJG.831078","DOIUrl":"https://doi.org/10.36890/IEJG.831078","url":null,"abstract":"We charecterize three-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are gradient Yamabe solitons and gradient Einstein solitons respectively.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45336761","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
Remarks on Scalar Curvature and Concircular Field Equation 关于标量曲率与简明场方程的注记
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-03-30 DOI: 10.36890/IEJG.906792
Ramesh Sharma, Sharief Deshmukh
{"title":"Remarks on Scalar Curvature and Concircular Field Equation","authors":"Ramesh Sharma, Sharief Deshmukh","doi":"10.36890/IEJG.906792","DOIUrl":"https://doi.org/10.36890/IEJG.906792","url":null,"abstract":"We show that the scalar curvature of a Riemannian manifold M is constant if it satisfies (i) the concircular field equation and M is compact, (ii) the special concircular field equation. Finally, we show that, if a complete connected Riemannian manifold admits a concircular non-isometric vector field leaving the scalar curvature invariant, and the conformal function is special concircular, then the scalar curvature is a constant.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42376435","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
Remarks on Einstein solitons with certain types of vector field 关于具有某些类型矢量场的爱因斯坦孤子的注记
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-03-30 DOI: 10.36890/IEJG.859572
A. Blaga, D. Laţcu
{"title":"Remarks on Einstein solitons with certain types of vector field","authors":"A. Blaga, D. Laţcu","doi":"10.36890/IEJG.859572","DOIUrl":"https://doi.org/10.36890/IEJG.859572","url":null,"abstract":"We consider almost Einstein solitons ( V, λ ) in a Riemannian manifold when V is a gradient, a solenoidal or a concircular vector field. We explicitly express the function λ by means of the gradient vector field V and illustrate the result with suitable examples. Moreover, we deduce some geometric properties when the Ricci curvature tensor of the manifold satisfies certain symmetry conditions.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45373565","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
Canal surface whose center curve is a hyperbolic curve with hyperbolic frame 中心曲线为双曲框架双曲曲线的运河曲面
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-03-30 DOI: 10.36890/IEJG.829766
A. Uçum
{"title":"Canal surface whose center curve is a hyperbolic curve with hyperbolic frame","authors":"A. Uçum","doi":"10.36890/IEJG.829766","DOIUrl":"https://doi.org/10.36890/IEJG.829766","url":null,"abstract":"In this paper, we obtain the parametrization of the canal surfaces whose center curves are the hyperbolic curves on the hyperbolic space H 2 in E 31 . The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10]. Then, the parallel surface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of these surfaces such that Weingarten surface, ( X, Y ) -Weingarten surface and linear Weingarten surface.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41422262","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
Hyperbolic Raisa Orbits of the Second Order in an Extended Hyperbolic Plane 扩展双曲平面上的二阶双曲Raisa轨道
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-03-29 DOI: 10.36890/IEJG.904467
L. Romakina
{"title":"Hyperbolic Raisa Orbits of the Second Order in an Extended Hyperbolic Plane","authors":"L. Romakina","doi":"10.36890/IEJG.904467","DOIUrl":"https://doi.org/10.36890/IEJG.904467","url":null,"abstract":"In this paper, we study conics, which are invariant under the hyperbolic inversion with respect to the absolute of an extended hyperbolic plane H of curvature radius ρ, ρ ∈ R+. They are called the hyperbolic Raisa Orbits of the second order. We prove that each hyperbolic Raisa Orbits of the second order in H belongs to one of four conics types of this plane. These types are as follows: the bihyperbolas of one sheet; the hyperbolas; the hyperbolic parabolas of one sheet and two branches; the elliptic cycles of radius πρ/4. The family of all hyperbolic Raisa Orbits from the family of all bihyperbolas of one sheet (or all hyperbolas) defined exactly up to motions, is one-parametric. The family of all hyperbolic Raisa Orbits from the family of all hyperbolic parabolas of one sheet and two branches (or all elliptic cycles) contains a unique conic defined exactly up to motions.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46295040","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
Splitting of the Einstein Field Equations with Respect to the $(1+1+3)$ Threading of a $5D$ Universe 关于$5D$宇宙的$（1+1+3）$线程的爱因斯坦场方程的分裂
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-03-24 DOI: 10.36890/IEJG.902162
A. Bejancu, H. Farran
{"title":"Splitting of the Einstein Field Equations with Respect to the $(1+1+3)$ Threading of a $5D$ Universe","authors":"A. Bejancu, H. Farran","doi":"10.36890/IEJG.902162","DOIUrl":"https://doi.org/10.36890/IEJG.902162","url":null,"abstract":"We obtain a new and simple splitting of Einstein field equations with respect to the (1 + 1 + 3) threading of a 5 D universe ( ¯ M, ¯ g ) . The study is based on the spatial tensor fields and on the Riemannian spatial connection, which behave as 3 D geometric objects. All the equations are expressed with respect to the adapted frame field and the adapted coframe field induced by the (1 + 1 + 3) threading of ( ¯ M, ¯ g ) . In particular, we obtain the splitting of the Einstein field equations in a 5 D Robertson-Walker universe.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47686500","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 Homogeneous Randers Metrics 关于齐次兰德指标
IF 0.7
International Electronic Journal of Geometry Pub Date : 2021-03-22 DOI: 10.36890/IEJG.797112
A. Sadighi, M. Toomanian, B. Najafi
{"title":"On Homogeneous Randers Metrics","authors":"A. Sadighi, M. Toomanian, B. Najafi","doi":"10.36890/IEJG.797112","DOIUrl":"https://doi.org/10.36890/IEJG.797112","url":null,"abstract":"In this paper, we study the curvature features of the class of homogeneous Randers metrics. For these metrics, we first find a reduction criterion to be a Berwald metric based on a mild restriction on their Ricci tensors. Then, we prove that every homogeneous Randers metric with relatively isotropic (or weak) Landsberg curvature must be Riemannian. This provides an extension of well-known Deng-Hu theorem that proves the same result for a homogeneous Berwald-Randers metric of non-zero flag curvature.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43584458","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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