On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold
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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.
KeywordsVector Field Singular Point Euler Characteristic Arbitrary Vector Oriented Manifold
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