2017
Том 69
№ 9

All Issues

On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold

Girik E. A.

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Abstract

We study the possibility of constructing locally gradient and arbitrary vector fields with a given set of singular points on a two-dimensional closed oriented manifold. The sum of the indices of the vector field at these points is equal to the Euler characteristic of the manifold.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 12, pp 1920-1923.

Citation Example: Girik E. A. On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold // Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1706–1709.

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