Warped products in Riemannian manifolds

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 of B. Y. Chen for the case of immersions into space forms. Finally we give an application where the target manifold is the Clifford torus.

10 pages, to appear in the Bulletin of the Australian Mathematical Society

References in corpus (1)

• A survey on geometry of warped product submanifolds

Cited by in corpus (1)

• On the estimates of warping functions on isometric immersions