On the curvature of a reductive homogeneous spaceG/H associated to a compact lie groupG

Abstract

By the use of the Radon-Nikodym derivative of exponential mappings the curvature tensor of a general reductive homogeneous space G/H in which G is a compact connected Lie group is presented. Again using that derivative and also the results of the variation calculus due to M. Morse applied to the length of geodesics, it is shown in § 2 that the diameter of a Riemann symmetric homogeneous space G/H in which G is a compact semi-simple Lie group is less than $$2\sqrt {n - 1} \pi $$ where n=dimG.