Uniqueness of the singular points of vector fields on Riemannian manifolds under the γ-condition

This paper is concerned with the problem of the uniqueness of singular points of vector fields on Riemannian manifolds. The radii of the uniqueness balls of the singular points of vector fields are estimated under the assumption that the vector fields satisfy the γ-condition, and the results due to Wang and Han in [Criterion α and Newton's method under weak conditions, Chinese J. Numer. Appl. Math. 19(2) (1997) 96–105] are extended. Moreover, applications to analytic vector fields are given.