Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-22T12:33:00.153Z Has data issue: false hasContentIssue false

Isometry invariant closed geodesic on a nonpositively curved manifold

Published online by Cambridge University Press:  22 January 2016

Tetsunori Kurogi*
Affiliation:
Department of Mathematics Faculty of Education, Fukui University, Fukui, 910, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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), 124126.Google Scholar
[ 4 ] Kurogi, T., Riemannian manifolds admitting some geodesies II, ibid., 52 (1976), 79.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), 207223.CrossRefGoogle Scholar
[ 6 ] Grove, K., Isometry invariant geodesic, Topology, 13 (1974), 281292.CrossRefGoogle Scholar
[ 7 ] Grove, K. and Tanaka, M., On the number of invariant closed geodesies, Acta Math., 140 (1978), 3348.CrossRefGoogle Scholar
[ 8 ] Ozols, V., Critical point of the displacement function of an isometry, J. Differential Geom., 3 (1969), 411432.CrossRefGoogle Scholar
[ 9 ] Sunada, T., Closed geodesies in locally symmetric space, Tohoku Math. J., 30 (1978), 5968.CrossRefGoogle Scholar
[10] Sunada, T., Trace formula and heat equation asymptotic for a nonpositively curved manifold, Amer. J. Math., 103 (1982), 411435.Google Scholar
[11] Tanaka, M., On the existence of infinitely many isometry invariant geodesies, J. Differential Geom., 17 (1982), 171184.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