Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (2): 586-604.doi: 10.1016/S0252-9602(12)60041-1

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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).

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

CLC Number: 

  • 30G35
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