A Laplace operator on complex Finsler manifolds

Abstract

In this paper, we give the Laplace operator by defining a global inner product of (p,q) differential forms on strongly pseudoconvex compact complex Finsler manifolds, which can be regarded as an extension of that on Hermitian manifolds. Moreover, we derive the local coordinate expression of the Laplace operator. Finally, we prove that the Laplace operator is an elliptic self-adjoint operator and Hodge decomposition theorem holds.