Mergulhos equivariantes de variedades Kahlerianas Simétricas

Abstract

In this work we investigate some characteristics of the equivariant embeddings of a symmetric Kahlerian manifold. We use the Theorem of Wallach-Cartan to characterize these embeddings in the case of CP" and SO(2n)/U(n) and verify that if a equivariant embedding has parallel plurimean curvature then it's the extrinsic symmetric one. We use the standard embedding of CP" to prove that if a complex submanifold of CP" has parallel plurimean curvature, then it's the totally geodesics. We propos a new equivariant embedding, the p-embedding, for any hermitian symmetric space and verify that, at least when the rank is one, the plurimean curvature is not parallel.