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Compact Riemannian Manifolds with Homogeneous Geodesics

2009
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Symmetry, Integrability and Geometry: Methods and Applications
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A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some sufficient conditions for existence and non-existence of an invariant metric $g$ with homogeneous geodesics on a homogeneous space of a compact Lie group $G$. We give a classification of compact simply connected GO-spaces $(M = G/H,g)$ of positive Euler

doi:10.3842/sigma.2009.093
fatcat:zqp5nlmwxzgbzg4dipad44y5se