A vanishing theorem on Kaehler Finsler manifolds

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□h and complex vertical Laplacian □v□v on the holomorphic tangent bundle T1,0MT1,0M of M  , and then we obtain a precise relationship among □h,□v□h,□v and the Hodge–Laplace operator △ on (T1,0M,〈⋅,⋅〉)(T1,0M,〈⋅,⋅〉), where 〈⋅,⋅〉〈⋅,⋅〉 is the induced Hermitian metric on T1,0MT1,0M by F. As an application, we prove a vanishing theorem of holomorphic p-forms on M under the condition that F is a Kaehler Finsler metric on M.