A vanishing theorem on Kaehler Finsler manifolds

摘要

Let M be a connected compact complex manifold endowed with a strongly pseudoconvex complex Finsler metric F. In this paper, we first define the complex horizontal Laplacian h and complex vertical Laplacian rectangle(v) on the holomorphic tangent bundle (TM)-M-1.0 of M, and then we obtain a precise relationship among rectangle(h), rectangle(v), and the Hodge-Laplace operator Delta on ((TM)-M-1.0, <.,.>), where <.,.>) is the induced Hermitian metric on (TM)-M-1.0 by F. As an application, we prove a vanishing theorem of holornorphic p-forms on M under the condition that F is a Kaehler Finsler metric on M.