球空间中具有拟平行第二基本形式的超曲面

doi:10.12677/PM.2023.134112

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球空间中具有拟平行第二基本形式的超曲面
Hypersurfaces with Quasi-Parallel SecondBasic Form in Spherical Space

DOI: 10.12677/PM.2023.134112, PDF, HTML,
作者: 苏峰：云南师范大学数学学院，云南昆明
关键词: 几何；超曲面；拟平行；第二基本形式；MO^¨bius形式；MO^¨bius Geometry； Hypersurface； Quasi-Parallel； MO^¨bius Second Fundamental Form； MO^¨bius Form

摘要: 设x : Mⁿ→ Sⁿ⁺¹为黎曼流形到单位球空间中等距浸入, g和B分别为x的莫比乌斯度量和莫比乌斯第二基本形式, R 为g诱导的曲率张量. 本文研究满足条件RB = 0的超曲面, 获得了几个初步的结果.

Abstract: Let x : Mⁿ→ Sⁿ⁺¹ be isometri immersion of Riemannian manifold into unit sphere space, and g and B be Mobius metric and Mobius second fundamental form of x respectively R is a curvature tensor induced by g. In this paper, we study the hypersurface operator satisfying the condition RB = 0, and obtain some preliminary results.

文章引用：苏峰. 球空间中具有拟平行第二基本形式的超曲面[J]. 理论数学, 2023, 13(4): 1062-1072. https://doi.org/10.12677/PM.2023.134112

参考文献

[1]	Wang, C.P. (1998) Moebius Geometry of Submanifolds in sⁿ. Manuscripta Mathematica, 96, 517-534. https://doi.org/10.1007/s002290050080
[2]	Guo, Z., Fang, J.B. and Lin, L.M. (2011) Hypersurfaces with Isotropic Blaschke Tensor. Journal of the Mathematical Society of Japan, 63, 1155-1186. https://doi.org/10.2969/jmsj/06341155
[3]	Hu, Z.J. and Li, H.Z. (2004) Classification of Hypersurfaces with Parallel Mobius Second Fundamental Form in Sn+1. Science China-Mathematics, 47, 417-430.

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