On geodesic graphs of Riemannian g.o. spaces

Abstract.

We study homogeneous Riemannian manifolds (G / H, g) on which every geodesic is an orbit of a one-parameter subgroup of G. We analyze the algebraic structure of certain minimal sets of vectors of the corresponding Lie algebra g (called “geodesic graphs”) which generate all geodesics through a fixed point. We are particularly interested in the case when the geodesic graphs are of non-linear character. Some structural theorems, many examples and also open problems are presented.