Lagrangian submanifolds with prescribed second fundamental form

Abstract

We classify Lagrangian submanifolds of complex space forms, whose second fundamental form can be written in a certain way, depending on a real parameter. For some special values of this parameter, the resulting submanifolds are ideal in the sense that they realize equality in an inequality for a Chen's delta-curvature.

arXiv comment8 pages. To appear in the Proceedings of Pure and Applied Differential Geometry PADGE 2012 - in honor of Franki Dillen