Vector fields on nonorientable surfaces

Abstract

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 .S ome 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 Mobius strip supports the nontriviality of the concepts introduced in this paper.