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Abstract and Applied Analysis
Volume 2014, Article ID 326434, 11 pages
http://dx.doi.org/10.1155/2014/326434
Research Article

Global Regularity for the -Equation on Manifolds of Arbitrary Codimension

1Mathematics Department, Faculty of Science, King Abdulaziz University, North Jeddah, Jeddah 21589, Saudi Arabia
2Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
3Mathematics Department, Faculty of Science, Minia University, El-Minia 61915, Egypt

Received 9 April 2014; Accepted 12 May 2014; Published 12 June 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Shaban Khidr and Osama Abdelkader. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a compact manifold of -codimension and -dimension in a complex manifold of complex dimension . In this paper, assuming that satisfies condition for some with , we prove an -existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for -forms on .