Twisted Hypersurfaces in Euclidean 5-Space

被引：15
|
作者：
Li, Yanlin [1 ,2 ]
Guler, Erhan [3 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
[2] Hangzhou Normal Univ, Key Lab Cryptog Zhejiang Prov, Hangzhou 311121, Peoples R China
[3] Bartın Univ, Fac Sci, Dept Math, Kutlubey Campus, TR-74100 Bartin, Turkiye
来源：
MATHEMATICS | 2023年 / 11卷 / 22期
关键词：
Euclidean five-space; twisted hypersurfaces family; Gauss map; mean curvature; Gauss-Kronecker curvature; Cayley-Hamilton theorem; Laplace-Beltrami operator; GAUSS MAP; ROTATION SURFACES; HELICOIDAL SURFACES; RULED SURFACES; BOURS THEOREM; MINKOWSKI; EXTENSION; OPERATOR; SPACE;
D O I：
10.3390/math11224612
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The twisted hypersurfaces x with the (0,0,0,0,1) rotating axis in five-dimensional Euclidean space E-5 is considered. The fundamental forms, the Gauss map, and the shape operator of x are calculated. In E-5, describing the curvatures by using the Cayley-Hamilton theorem, the curvatures of hypersurfaces x are obtained. The solutions of differential equations of the curvatures of the hypersurfaces are open problems. The umbilically and minimality conditions to the curvatures of x are determined. Additionally, the Laplace-Beltrami operator relation of x is given.
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页数：17
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