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| Laplacian on Complex Finsler Manifolds |
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Citation： |
Jinxiu XIAO,Tongde ZHONG,Chunhui QIU.Laplacian on Complex Finsler Manifolds[J].Chinese Annals of Mathematics B,2011,32(4):507~520 |
| Page view： 2064
Net amount： 1222 |
Authors： |
Jinxiu XIAO; Tongde ZHONG; Chunhui QIU; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10871145, 10771174) and the
Doctoral Program Foundation of the Ministry of Education of China (No. 2009007Q110053). |
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| Abstract： |
In this paper, the Laplacian on the holomorphic tangent bundle T1,0M of
a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric
is defined and its explicit expression is obtained by using the Chern Finsler connection
associated with (M,F). Utilizing the initiated “Bochner technique”, a vanishing theorem
for vector fields on the holomorphic tangent bundle T1,0M is obtained. |
Keywords： |
Laplacian, Strongly pseudoconvex complex Finsler metric, Chern
Finsler connection |
Classification： |
32Q99, 53C56 |
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