Warped products in Riemannian manifolds

Authors

  • K. S. Park Seoul National University

Keywords:

warped products, squared mean curvature, warping function, second fundamental form

Abstract

In this paper we prove two inequalities relating the warping function to various curvature terms, for warped products isometrically immersed in Riemannian manifolds. This extends work by B. Y. Chen [‘On isometric minimal immersions from warped products into real space forms’, Proc. Edinb. Math. Soc. (2) 45(3) (2002), 579–587 and ‘Warped products in real space forms’, Rocky Mountain J. Math. 34(2) (2004), 551–563] for the case of immersions into space forms. Finally, we give an application where the target manifold is the Clifford torus. DOI:- 10.1017/S0004972714000549

Published

2014-09-20

Issue

Vol. 90 No. 3 (2014)

Section

Articles
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