Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T14:48:45.990Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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