Hyperholomorphic theory on kaehler manifolds

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