WARPED PRODUCTS IN RIEMANNIAN MANIFOLDS

Abstract

AbstractIn 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.