HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS

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

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