Geodesic
Periodic Orbits for Generalized Gradient Flows
Canadian mathematical bulletin, Tome 38 (1995) no. 1, pp. 117-119

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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.
DOI : 10.4153/CMB-1995-016-8
Mots-clés : 58F25 
Schwartzman, Sol. Periodic Orbits for Generalized Gradient Flows. Canadian mathematical bulletin, Tome 38 (1995) no. 1, pp. 117-119. doi: 10.4153/CMB-1995-016-8
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     title = {Periodic {Orbits} for {Generalized} {Gradient} {Flows}},
     journal = {Canadian mathematical bulletin},
     pages = {117--119},
     year = {1995},
     volume = {38},
     number = {1},
     doi = {10.4153/CMB-1995-016-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-016-8/}
}
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