Vector fields with a given set of singular points - Prishlyak, O. O. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
Theorems on the existence of vector fields with given sets of indexes of isolated singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a two-dimensional manifold, an index of an isolated singular point of the gradient field is not greater than one.