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 δ and δ on Kaehler manifolds w...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 δ and δ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace opeator is argued. Then, the Borel-Pompeiu formulas for W-valued functions are derived through designing a matrix Dirac operator D and a 2 × 2 matrix-valued invariant integral kernel with the Witt basis.展开更多
基金Project supported in part by the National Natural Science Foundation of China (10771174,10601040,10971170)Scientific Research Foundation of Xiamen University of Technology (700298)
文摘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 δ and δ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace opeator is argued. Then, the Borel-Pompeiu formulas for W-valued functions are derived through designing a matrix Dirac operator D and a 2 × 2 matrix-valued invariant integral kernel with the Witt basis.
