A Laplace operator on complex Finsler manifolds

Author(s)
Hongjun Li, Chunhui Qiu, Weixia Zhu
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.

Organisation(s)
Department of Mathematics
External organisation(s)
Xiamen University
Journal
Differential Geometry and Its Applications
Volume
54
Pages
437-447
No. of pages
11
ISSN
0926-2245
DOI
https://doi.org/10.1016/j.difgeo.2017.07.007
Publication date
10-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
101009 Geometry
Keywords
ASJC Scopus subject areas
Analysis, Geometry and Topology, Computational Theory and Mathematics
Portal url
https://ucris.univie.ac.at/portal/en/publications/a-laplace-operator-on-complex-finsler-manifolds(612c0351-f3aa-4a94-84ad-7401dbff693f).html