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

Authors

  • E. A. Girik

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.

Published

25.12.1993

Issue

Section

Short communications

How to Cite

Girik, E. A. “On the Existence of Vector Fields With a Given Set of Singular Points on a Two-Dimensional Closed Oriented Manifold”. Ukrains’kyi Matematychnyi Zhurnal, vol. 45, no. 12, Dec. 1993, pp. 1706–1709, https://umj.imath.kiev.ua/index.php/umj/article/view/5980.