On the holomorphic curvature of complex Finsler hypersurfaces

Abstract

Following the study of real hypersurfaces of Finsler spaces, in this paper, we analyze the holomorphic hypersurfaces associated with a complex Finsler space (M, F) as holomorphic subspaces of complex codimension one. In this sense, the induced complex Finsler metric, the induced nonlinear connection, and, respectively, the linear connection and the equations of the holomorphic curvature are investigated. Moreover, based on the Gauss, Codazzi, and Ricci equations we find the link between the holomorphic curvatures of the holomorphic hypersurface and the Finsler space (M, F), and the conditions under which the holomorphic hypersurface is totally geodesic, c-totally geodesic or generalized Einstein.