MINIMAL IMMERSIONS OF KÄHLER MANIFOLDS INTO EUCLIDEAN SPACES

Abstract

It is proved here that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler-manifold into an Euclidean space must be totally geodesic. As an application, it is shown that an open subset of the real hyperbolic plane RH2 cannot be minimally immersed into the Euclidean space. As another application, a proof is given that if an irreducible Kähler manifold is minimally immersed in a Euclidean space, then its restricted holonomy group must be U(n), where n = dimCM. 2000 Mathematics Subject Classification 53B25 (primary); 53C42 (secondary).