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arXiv · 1706.09618

Homogeneous manifolds whose geodesics are orbits. Recent results and some open problems

Andreas Arvanitoyeorgos
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Abstract

A homogeneous Riemannian manifold $(M=G/K, g)$ is called a space with homogeneous geodesics or a $G$-g.o. space if every geodesic $γ(t)$ of $M$ is an orbit of a one-parameter subgroup of $G$, that is $γ(t) = \exp(tX)\cdot o$, for some non zero vector $X$ in the Lie algebra of $G$. We give an exposition on the subject, by presenting techniques that have been used so far and a wide selection of previous and recent results. We also present some open problems.

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Andreas Arvanitoyeorgos. 2017-06-29. Homogeneous manifolds whose geodesics are orbits. Recent results and some open problems. https://arxiv.org/abs/1706.09618

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