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Laplacians on the holomorphic tangent bundle of a Kaehler manifold

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Abstract

Let M be a connected complex manifold endowed with a Hermitian metric g. In this paper, the complex horizontal and vertical Laplacians associated with the induced Hermitian metric 〈·, ·〉 on the holomorphic tangent bundle T 1,0 M of M are defined, and their explicit expressions are obtained. Using the complex horizontal and vertical Laplacians associated with the Hermitian metric 〈·, ·〉 on T 1,0 M, we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0 M under the condition that g is a Kaehler metric on M.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    ChunPing Zhong

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  1. ChunPing Zhong
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Correspondence to ChunPing Zhong.

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Dedicated to Professor ZHONG TongDe on the occasion of his 80th birthday

This work was supported by the Program for New Century Excellent Talents in Fujian Province and National Natural Science Foundation of China (Grant Nos. 10601040, 10971170)

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Zhong, C. Laplacians on the holomorphic tangent bundle of a Kaehler manifold. Sci. China Ser. A-Math. 52, 2841–2854 (2009). https://doi.org/10.1007/s11425-009-0174-8

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  • DOI: https://doi.org/10.1007/s11425-009-0174-8

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