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Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1920–1923 | Cite as

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

  • E. A. Girik
Brief Communications
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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.

Keywords

Vector Field Singular Point Euler Characteristic Arbitrary Vector Oriented Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. T. Fomenko,Differential Geometry and Topology. Additional Chapters [in Russian], Moscow University, Moscow (1983).Google Scholar
  2. 2.
    A. S. Mishchenko and A. T. Fomenko,A Course of Differential Geometry and Topology [in Russian], Moscow University, Moscow (1980).Google Scholar
  3. 3.
    J. Milnor and A. Wallace,Differential Topology [Russian translation], Mir, Moscow (1972).Google Scholar
  4. 4.
    H. Poincaré,Selected Works [Russian translation], Nauka, Moscow (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • E. A. Girik
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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