×

zbMATH — the first resource for mathematics

On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold. (English. Russian original) Zbl 0830.57017
Ukr. Math. J. 45, No. 12, 1920-1923 (1993); translation from Ukr. Mat. Zh. 45, No. 12, 1706-1709 (1993).
Summary: 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.

MSC:
57R25 Vector fields, frame fields in differential topology
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. T. Fomenko,Differential Geometry and Topology. Additional Chapters [in Russian], Moscow University, Moscow (1983). · Zbl 0517.53001
[2] A. S. Mishchenko and A. T. Fomenko,A Course of Differential Geometry and Topology [in Russian], Moscow University, Moscow (1980). · Zbl 0524.53001
[3] J. Milnor and A. Wallace,Differential Topology [Russian translation], Mir, Moscow (1972).
[4] H. Poincar?,Selected Works [Russian translation], Nauka, Moscow (1972).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.