复Finsler流形上的Hodge-Laplace算子(英文)

Hodge-Laplace Operator on Complex Finsler Manifolds

本文定义了强拟凸复Finsler流形上的Hodge-Laplace算子,并给出其水平部分的局部坐标表示．

A Hodge-Laplace operator is defined on a compact strongly pseudoconvex complex Finsler manifold （M, F）, it reduces to the classical Hodge-Laplace operator in Hermitian cases. The key point of defining this Hodge-Laplace operator is to define a global inner product on the base manifold M. We do this by pulling the differential forms of type-（p, q） on M back to the projectivized tangent bundle PTM of M and then using the natural Hermitian inner product on PTM to obtain a global inner product on M.