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Homogeneous manifolds whose geodesics are orbits. Recent results and some open problems. (arXiv:1706.09618v1 [math.DG])

来源于:arXiv
A homogeneous Riemannian manifold $(M=G/K, g)$ is called a space with homogeneous geodesics or a $G$-g.o. space if every geodesic $\gamma (t)$ of $M$ is an orbit of a one-parameter subgroup of $G$, that is $\gamma(t) = \exp(tX)\cdot o$, 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. 查看全文>>