On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold - Girik, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
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.