2009•Journal of Anhui Normal UniversityRequires access

Sufficient Conditions for Totally Geodesic Submanifolds in Space Forms

Song Wei-dong

Abstract

In this paper,the author gives sufficient conditions for compact minimal submanifolds in space forms to be totally geodesic ones;Let Mn(n2) be a compact minimal submanifold in a space form Nn+p(c), if one of the following conditions holds:(i) R(n2-n+1-2n)c2nQ;(ii) K34n[n(n-1)c-R],then Mn must be totally geodesic submaniford.

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Key concepts: Submanifold, Totally geodesic, Geodesic, Space (punctuation), Pure mathematics, Mathematics, Space form, Mathematical analysis