A Comprehensive Survey on Parallel Submanifolds in Riemannian and Pseudo-Riemannian Manifolds

被引：1

作者：

Chen, Bang-Yen ^{[1
]}

机构：

[1] Michigan State Univ, Dept Math, 619 Red Cedar Rd, E Lansing, MI 48824 USA

来源：

AXIOMS | 2019年 / 8卷 / 04期

关键词：

parallel submanifold; real space form; complex space form; totally real submanifolds; Kaehler submanifolds; light cone; Thurston 3D geometries; Bianchi-Cartan-Vranceasu spaces; MEAN-CURVATURE VECTOR; MARGINALLY TRAPPED SURFACES; INDEFINITE SPACE-FORMS; PLANAR NORMAL SECTIONS; REAL SUB-MANIFOLDS; COMPLETE CLASSIFICATION; DIFFERENTIAL GEOMETRY; LORENTZ SURFACES; SYMMETRIC SUBMANIFOLDS; KAEHLER SUBMANIFOLDS;

D O I：

10.3390/axioms8040120

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden-Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifolds form an important class of Riemannian submanifolds since extrinsic invariants of a parallel submanifold do not vary from point to point. In this paper, we provide a comprehensive survey on this important class of submanifolds.

引用

页数：64

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