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On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold

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Abstract

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.

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References

  1. A. T. Fomenko,Differential Geometry and Topology. Additional Chapters [in Russian], Moscow University, Moscow (1983).

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  2. A. S. Mishchenko and A. T. Fomenko,A Course of Differential Geometry and Topology [in Russian], Moscow University, Moscow (1980).

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  3. J. Milnor and A. Wallace,Differential Topology [Russian translation], Mir, Moscow (1972).

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  4. H. Poincaré,Selected Works [Russian translation], Nauka, Moscow (1972).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    E. A. Girik

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  1. E. A. Girik
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1706–1709, December, 1993.

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Girik, E.A. On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold. Ukr Math J 45, 1920–1923 (1993). https://doi.org/10.1007/BF01061363

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  • DOI: https://doi.org/10.1007/BF01061363

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