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Isometric rigidity of submanifolds in products of space forms

Abstract

The study of rigidity and isometric deformations of submanifolds with dimension greater than or equal to three has received the attention of may generations of geometers, since the pioneering work of Beez-Killing, Sbrana and Cartan, among others. Recent contributions of many authors, which yielded Bonnet-like theorems for more general spaces, have paved the way for developing a theory of isometric deformations of submanifolds of such spaces. A few results along this line have been recently obtained by the proponent, in particular, for the case of hypersurfaces of a product of a space form and the real line. Our aim in this project is to develop a general theory of rigidity of submanifolds in such spaces and, more generally, in products of space forms, in the light of a Bonnet theorem recently obtained for such spaces. (AU)

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