No CrossRef data available.
Published online by Cambridge University Press: 22 January 2016
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.