Marcos Dajczer
(IMPA, Brasil)

Abstract: A basic problem in submanifold theory is to decide if an isometric immersion of a given Riemannian manifold into a space form is unique, up to rigid motions. If this is the case, then the immersion is called rigid. If the immersion is not rigid, then it is a fundamental problem to determine all of its isometric deformations. The local problem for hypersurfaces was mostly solved by Sbrana and Cartan more than a century ago. A solution to the problem for compact hypersurfaces was given by Sacksteder and by Dajczer-Gromoll in the complete case. I will discuss a contribution to the solution of the global problem in codimension two by means of new classes of minimal immersions. This is joint work with Th. Vlachos.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.