Laplacians for the holomorphic tangent bundles with g-nature metrics on complex Finsler manifolds

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

Let M be a strongly pseudoconvex compact complex Finsler manifold. We first introduce a class of g-nature metric G(a,b) for the slit holomorphic tangent bundle (M) over tilde = (TM)-M-1,0\{0} on M. Then, we define the complex horizontal Laplacian square(h), and complex vertical Laplacian square(v) and obtain a precise relationship among square(h), square(v) and the Hodge-Laplace operator square on ((M) over tilde, G(a,b)). As an application, we discuss the holomorphic Killing vector fields associated to G(a,b).

Organisation(s)
Department of Mathematics
External organisation(s)
Xiamen University
Journal
International Journal of Mathematics
Volume
28
No. of pages
19
ISSN
0129-167X
DOI
https://doi.org/10.1142/S0129167X17400110
Publication date
08-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
101009 Geometry
Keywords
ASJC Scopus subject areas
Mathematics(all)
Portal url
https://ucris.univie.ac.at/portal/en/publications/laplacians-for-the-holomorphic-tangent-bundles-with-gnature-metrics-on-complex-finsler-manifolds(f229a2c6-982b-48e1-ba33-e4a75b92b60a).html