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Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions

Published online by Cambridge University Press:  19 July 2001

BANG-YEN CHEN
BANG-YEN CHEN
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027, USA; e-mail: bychen@math.msu.edu
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Abstract

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First we define the notion of k-Ricci curvature of a Riemannian n-manifold. Then we establish sharp relations between the k-Ricci curvature and the shape operator and also between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Several applications of such relationships are also presented.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 1 , March 1999 , pp. 33 - 41
Copyright
1999 Glasgow Mathematical Journal Trust