数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 586-604.doi: 10.1016/S0252-9602(12)60041-1

• 论文 • 上一篇    下一篇

HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS

汤冬梅|钟同德|邱春晖   

  1. Department of Mathematics and Physics, Xiamen University of Technology, Xiamen 361024, China； School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2009-10-20 修回日期:2011-03-18 出版日期:2012-03-20 发布日期:2012-03-20
  • 基金资助:

    Project supported in part by the National Natural Science Foundation of China (10771174, 10601040, 10971170) and Scientific Research Foundation of Xiamen University of Technology (700298).

HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS

 TANG Dong-Mei, ZHONG Tong-De, QIU Chun-Hui   

  1. Department of Mathematics and Physics, Xiamen University of Technology, Xiamen 361024, China； School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2009-10-20 Revised:2011-03-18 Online:2012-03-20 Published:2012-03-20
  • Supported by:

    Project supported in part by the National Natural Science Foundation of China (10771174, 10601040, 10971170) and Scientific Research Foundation of Xiamen University of Technology (700298).

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摘要：

First of all, using the relations (2.3), (2.4), and (2.5), we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators ∂and ∂^ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace operator is argued. Then, the Borel-Pompeiu formulas for Wn-valued functions are derived through designing a matrix Dirac operator D and a 2× 2 matrix–valued invariant integral kernel with the Witt basis.

关键词: Kaehler manifolds, complex Clifford algebra, Witt basis, matrix Dirac op-erator, matrix Cauchy-Dirac kernel

Abstract:

First of all, using the relations (2.3), (2.4), and (2.5), we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators ∂and ∂^ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace operator is argued. Then, the Borel-Pompeiu formulas for Wn-valued functions are derived through designing a matrix Dirac operator D and a 2× 2 matrix–valued invariant integral kernel with the Witt basis.

Key words: Kaehler manifolds, complex Clifford algebra, Witt basis, matrix Dirac op-erator, matrix Cauchy-Dirac kernel

中图分类号: 

  • 30G35
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