强Khler-Finsler流形上(p,q)形式的中值Laplace算子(英文)

Mean-Value Laplacian for (p, g)-forms on Strongly Khler-Finsler Manifolds

本文给出了强Khler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等。与Khler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强Khler-Finsler流形上的逆变密切Khler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强Khler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广。

Some properties of the mean-value Laplacian for functions of strongly Kahler-Finsler manifolds such as self-adjointness and the divergence form are given. Differ from the classical case as in Kahler manifold using contravariant fundamental tensor and using its variance in Finsler manifold as density to define the pointwise and global inner product, the authors using contravariant osculating Kahler metric as density to define the pointwise and global inner product, and then define the Hodge-Laplace operator for strongly Kahler-Finsler manifolds, which may be regarded as the extension of mean-value Laplacian for functions.