Acta mathematica scientia, Series B >
HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS
Received date: 2009-10-20
Revised date: 2011-03-18
Online 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).
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.
TANG Dong-Mei , ZHONG Tong-De , QIU Chun-Hui . HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS[J]. Acta mathematica scientia, Series B, 2012 , 32(2) : 586 -604 . DOI: 10.1016/S0252-9602(12)60041-1
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