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Periodic Orbits for Generalized Gradient Flows

Published online by Cambridge University Press:  20 November 2018

Sol Schwartzman
Sol Schwartzman*
Affiliation:
University of Rhode Island, Kingston, Rhode Island, U.S.A.
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Abstract

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Let Mn be an n-dimensional compact oriented connected Riemannean manifold. It is proved that either of the following conditions is sufficient to insure that the flow defined by a generalized gradient vector field in Mn has either a stationary point or a periodic orbit:

  • a)Mn is the product of a circle with an (n — 1 ) dimensional manifold of non-zero Euler characteristic.

  • b)The (n — 1) dimensional Stiefel-Whitney class of Mn is different from zero and in addition Mn possesses no one-dimensional 2-torsion.

Keywords

58F25

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 117 - 119
Copyright
Copyright © Canadian Mathematical Society 1995

References

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