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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)
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##### 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).
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