International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 3, Pages 133-152

Vector fields on nonorientable surfaces

Ilie Barza1 and Dorin Ghisa2

1Department of Engineering Sciences, Physics and Mathematics, Karlstad University, Karlstad, S-651 88, Sweden
2Department of Mathematics, Glendon College, York University, 2275-Bayview Avenue, Toronto M4N 3M6, Canada

Received 4 April 2002

Copyright © 2003 Ilie Barza and Dorin Ghisa. 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.


A one-to-one correspondence is established between the germs of functions and tangent vectors on a NOS X and the bi-germs of functions, respectively, elementary fields of tangent vectors (EFTV) on the orientable double cover of X. Some representation theorems for the algebra of germs of functions, the tangent space at an arbitrary point of X, and the space of vector fields on X are proved by using a symmetrisation process. An example related to the normal derivative on the border of the Möbius strip supports the nontriviality of the concepts introduced in this paper.