Holomorphic maps of K�hler manifolds with constrained energy density

Abstract

We consider holomorphic and antiholomorphic maps of Kahler manifoldsM andN withM compact. In view of bounds on the Ricci curvature ofM and the holomorphic bisectional curvature ofN, the energy density of the map is constrained to satisfy certain inequalities. One inequality implies that the map is constant. Another specifies the image ofM as a totally geodesic real surface of constant Gaussian curvature inN.