Abstract
A Simons type formula for submanifolds with parallel normalized mean curvature vector field (pnmc submanifolds) in the product spaces Sn×R, where Sn is the unit Euclidean sphere, is proved. As an application, an integral inequality for pnmc closed submanifolds in Sn×R is obtained. By this, it is shown that the sharpness in this inequality is attained, in the totally umbilical hypersurfaces, and in a certain family of standard tori of the form S1(1−r2)×Sn−1(r) with 0<r<1.
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