On the volume of certain manifolds with closed geodesics

It is proved that the ratio of the volume of a Riemannian manifold of cohomology typeCP² orCP³ for which all geodesics are closed and of length 2 to the volume of the standard sphere assumes a fixed value.Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 102–106