Parallel Codazzi tensors with submanifold applications

Author:

Gruber Anthony1ORCID

Affiliation:

1. Department of Mathematics and Statistics Texas Tech University Lubbock Texas USA

Abstract

AbstractA decomposition theorem is established for a class of closed Riemannian submanifolds immersed in a space form of the constant sectional curvature. In particular, it is shown that if M has nonnegative sectional curvature and admits a Codazzi tensor with “parallel mean curvature”, then M is locally isometric to a direct product of irreducible factors determined by the spectrum of that tensor. This decomposition is global when M is simply connected, and generalizes what is known for immersed submanifolds with parallel mean curvature vector.

Publisher

Wiley

Subject

General Mathematics

Reference19 articles.

1. Codazzi tensor fields and curvature operators

2. A note on Codazzi tensors

3. Submanifolds with parallel mean curvature vector in Riemannian and indefinite space forms;Chen B. Y.;Arab J. Math.,2010

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