Warped product structure of submanifolds with nonpositive extrinsic curvature in space forms

Luis A. Florit

Keywords: nonpositive extrinsic curvature | splitting | warped products

By means of a simple warped product construction we obtain examples of submanifolds with nonpositive extrinsic curvature and minimal index of relative nullity in any space form. We then use this to extend to arbitrary space forms four known splitting results for Euclidean submanifolds with nonpositive sectional curvature.

Anexos:

• warpedsplit.pdf