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| Bochner-Kodaira Techniqueson Kahler Finsler Manifolds |
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Citation： |
Jinxiu XIAO,Chunhui QIU,Tongde ZHONG.Bochner-Kodaira Techniqueson Kahler Finsler Manifolds[J].Chinese Annals of Mathematics B,2015,36(1):125~140 |
| Page view： 1589
Net amount： 1260 |
Authors： |
Jinxiu XIAO; Chunhui QIU; Tongde ZHONG; |
Foundation： |
the National Natural Science Foundation of China (No. 11712777) and the
Scientific Research Foundation of Shanghai University of Engineering Science (No. E1-0501-14-0112). |
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| Abstract： |
A horizontal Hodge Laplacian operator $\square_{\mathcal {H}}$ is
defined for Hermitian holomorphic vector bundles over PTM on
K\"{a}hler Finsler manifold, and the expression of
$\square_{\mathcal {H}}$ is obtained explicitly in terms of
horizontal covariant derivatives of the Chern-Finsler connection.
The vanishing theorem is obtained by using the $\partial_{\mathcal
{H}}\ov{\partial}_{\mathcal {H}}$-method on K\"{a}hler Finsler
manifolds. |
Keywords： |
Kahler Finsler manifold, Horizontal Hodge Laplacian operator,
Bochner-Kodaira technique |
Classification： |
32Q15, 53C55, 53C60 |
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