The k-Cauchy-Fueter complex, Penrose transformation and Hartogs phenomenon for quaternionic k-regular functions

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Wang, Wei

关键词: k-Cauchy-Fueter complex;    Penrose transformation;    Quaternionic k-regular functions;    Elliptic differential complex;    Non-homogeneous k-Cauchy-Fueter equations;    Hartogs phenomenon;    Integral representation formula;   

DOI  :  10.1016/j.geomphys.2009.11.011

来源: Elsevier

【 摘 要 】

By using complex geometric method associated to the Penrose transformation, we give a complete derivation of an exact sequence over C-4n, whose associated differential complex over H-n is the k-Cauchy-Fueter complex with the first operator D-0((k)) annihilating k-regular functions. D-0((I)) is the usual Cauchy-Fueter operator and 1-regular functions are quaternionic regular functions. We also show that the k-Cauchy-Fueter complex is elliptic. By using the fundamental solutions to the Laplacian operators of 4-order associated to the k-Cauchy-Fueter complex, we can establish the corresponding Bochner-Martinelli integral representation formula, solve the non-homogeneous k-Cauchy-Fueter equations and prove the Hartogs extension phenomenon for k-regular functions in any bounded domain. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free