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Vector fields on nonorientable surfaces

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  • Ilie Barza
  • Dorin Ghisa

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.

Suggested Citation

  • Ilie Barza & Dorin Ghisa, 2003. "Vector fields on nonorientable surfaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-20, January.
    • Handle: RePEc:hin:jijmms:392192
    DOI: 10.1155/S0161171203204038
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