International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 315754, 8 pages
doi:10.1155/2010/315754
Research Article

Abnormal Curves on the Goursat Systems of R 𝑛

Mohamad H. Cheaito and Hassan Zeineddine

Department of Mathematics, Faculty of Sciences, Lebanese University, Hadath, Lebanon

Received 9 May 2010; Accepted 27 December 2010

Academic Editor: Frédéric Robert

Copyright © 2010 Mohamad H. Cheaito and Hassan Zeineddine. 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

We study the abnormal and the rigid curves of the 2-distributions of 𝐑 𝑛 satisfying everywhere the Goursat condition. We give the directions for the rigid and the abnormal curves when the systems satisfy the strong Goursat condition or when they have a singularity of order 2 in each dimension.