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On a proof of divisibility lemma, I

Published online by Cambridge University Press:  22 January 2016

Y. Shikata  and
W. Klingenberg
Y. Shikata
Affiliation:
Department of Mathematics Faculty of Sciences Nagoya University, Chikusa-ku, Nagoya 464, Japan
W. Klingenberg
Affiliation:
Mathematisches Institut der Universität, Wegelerstrasse 10 5300 Bonn, Germany
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A method to show the existence of infinitely many closed geodesies on a manifold with non degenerate Riemannian metric is to use socalled divisibility lemma which is conjectured to hold in [K].

Our purpose in this series of papers is, then, to show first the divisibility lemma in a modified form on k-sphere Sk (k≧3) with (strongly) non degenerate Riemannian metric and to deduce the existence of infinitely many closed geodesies on Sk (k≧3) using the modified divisibility lemma by equivariant modifications of flows.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 100 , December 1985 , pp. 65 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[H] Hong, S. H., On equivariant Morse complex (to appear).Google Scholar
[K] Klingenberg, , Lectures on closed geodesies, Springer Verlag 1978.Google Scholar
[K-S] Klingenberg, W. and Shikata, Y., On a proof of divisibility lemma, Moscov Topology Symposium 1980 (also correction in 1984).Google Scholar
[Sch] Schwarz, A., Homology of the space of closed curves, Trudy Moscov. Mat Obsc, 9 (1960), 3–44.Google Scholar