Totally umbilical submanifolds in irreducible symmetric spaces

Bang‐Yen Chen; Paul Verheyen

doi:10.1017/s1446788700024885

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Totally umbilical submanifolds in irreducible symmetric spaces

Bang‐Yen Chen Paul Verheyen

Year: 1982 Journal: Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics Vol: 32 (3)Pages: 332-338 Publisher: Cambridge University Press

DOI: 10.1017/s1446788700024885

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Abstract

Abstract A submanifold of a Riemannian manifold is called a totally umbilical submanifold if its first and second fundamental forms are proportional. In this paper we prove the following best possible result.

Keywords:

Submanifold Mathematics Pure mathematics Manifold (fluid mechanics) Riemannian manifold Mathematical analysis

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Geometric Analysis and Curvature Flows

Physical Sciences → Mathematics → Applied Mathematics

Advanced Differential Geometry Research

Physical Sciences → Physics and Astronomy → Astronomy and Astrophysics

Point processes and geometric inequalities

Physical Sciences → Mathematics → Applied Mathematics

Totally umbilical submanifolds in irreducible symmetric spaces

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