Imersões PPMC em espaços hiperbólicos e imersões plurimínimas em espaços produto

Abstract

Let E"(c) be a space of constant sectional curvature c # 0. We prove that minimal or pluriminimal Kahler submanifolds in En(c) x JR are surfaces. For a pluriminimal immersed submanifold into CPn x R, there exists a dense open sub-set that it admits a foliation by holomorphics (or antiholomorphics) submanifolds of CPn . We investigate pluriminimal immersions of compact Kahler manifolds with first Chern class positive into CP" x R. In this case, it is holomorphic (an-tiholoforphic) in the first factor. In addition, for a half isotropic ppmc immersion of Kahler manifolds into hyperbolic space we have that either it is decomposable in Lorentz space, or it comes from ppmc immersion of Rn or it is immersion of surfa-ces with parallel mean curvature. We also prove that ppmc immersion of compact Kahler manifolds with positive first Chern class into hyperbolic space either it is decomposable in Lorentz space, or it comes from ppmc immersion of IR". Keywords: pluriminimal immersion, ppmc immersion, Kahler manifolds, pa-rallel plurimean curvature.