Critical point theory of symmetric functions and closed geodesics
The authors consider compact Riemannian manifolds which allow a map \(F\) of a sphere or a projective space into the manifold, which is injective on the homology level. Denote by \(l_{max}\) the maximal length of the image of a circle under \(F\) and by \(l_{min}\) the length of the shortest closed geodesic. In terms of the integer part \(p\) of the quotient \(l_{max}/l_{min}\) the authors obtain lower bounds for the number of geometrically distinct closed geodesics of length \(\leq l_{max}\) (which are called short closed geodesics). For certain values of \(p\) and certain topological types this gives an improvement of known results.
scientific article; zbMATH DE number 1019166
scientific article