HORIZONTALLY HOMOTHETIC HARMONIC MORPHISMS AND STABILITY OF TOTALLY GEODESIC SUBMANIFOLDS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 2, 2008, pp.493-511
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.2.493

Title & Authors

HORIZONTALLY HOMOTHETIC HARMONIC MORPHISMS AND STABILITY OF TOTALLY GEODESIC SUBMANIFOLDS

Yun, Gab-Jin; Choi, Gun-Don;

Yun, Gab-Jin; Choi, Gun-Don;

Abstract

In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of . We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, (P), is volume-stable in M. In case that P is a totally geodesic hypersurface the condition on the curvature can be weakened to Ricci curvature.

Keywords

harmonic morphism;horizontally homothetic;stable minimal submanifold;totally geodesic;

Language

English

Cited by

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