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Isometry invariant closed geodesic on a nonpositively curved manifold

Published online by Cambridge University Press:  22 January 2016

Tetsunori Kurogi
Tetsunori Kurogi*
Affiliation:
Department of Mathematics Faculty of Education, Fukui University, Fukui, 910, Japan
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In this paper we wish to study the isometry invariant geodesic on a non-positively curved manifold from a point of view of the displacement function.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 95 , September 1984 , pp. 91 - 102
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Klingenberg, W., Riemannian Geometry, Walter de Gruyter, 1982.Google Scholar
[ 2 ] Kobayashi, S., Transformation groups in differential geometry, Ergeb. der Math., Band, 70 (1972).Google Scholar
[ 3 ] Kurogi, T., Riemannian manifolds admitting some geodesies, Proc. Japan Acad., 50 (1974), 124–126.Google Scholar
[ 4 ] Kurogi, T., Riemannian manifolds admitting some geodesies II, ibid., 52 (1976), 7–9.Google Scholar
[ 5 ] Grove, K., Condition (C) for the energy integral on certain path spaces and applications to the theory of geodesies, J. Differential Geom., 8 (1973), 207–223.CrossRefGoogle Scholar
[ 6 ] Grove, K., Isometry invariant geodesic, Topology, 13 (1974), 281–292.CrossRefGoogle Scholar
[ 7 ] Grove, K. and Tanaka, M., On the number of invariant closed geodesies, Acta Math., 140 (1978), 33–48.CrossRefGoogle Scholar
[ 8 ] Ozols, V., Critical point of the displacement function of an isometry, J. Differential Geom., 3 (1969), 411–432.CrossRefGoogle Scholar
[ 9 ] Sunada, T., Closed geodesies in locally symmetric space, Tohoku Math. J., 30 (1978), 59–68.CrossRefGoogle Scholar
[10] Sunada, T., Trace formula and heat equation asymptotic for a nonpositively curved manifold, Amer. J. Math., 103 (1982), 411–435.Google Scholar
[11] Tanaka, M., On the existence of infinitely many isometry invariant geodesies, J. Differential Geom., 17 (1982), 171–184.CrossRefGoogle Scholar
[12] Tanaka, M., On the number of closed geodesies and isometry invariant geodesies, Preprint of Proceedings of Geodesic at Tokyo University, 1982.Google Scholar