Vector fields on nonorientable surfaces

Ilie Barza and Dorin Ghisa

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-20

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 . 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:392192

DOI: 10.1155/S0161171203204038

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