International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 3, Pages 133-152
Vector fields on nonorientable surfaces
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
bi-germs of functions, respectively, elementary fields of tangent
vectors (EFTV) on the orientable double cover of .
Some representation theorems for the algebra of germs of
functions, the tangent space at an arbitrary point of
, and the space of vector fields on 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.