Compact Riemannian manifolds with homogeneous geodesics.
Alekseevsky, Dmitrii V., Nikonorov, Yurii G. (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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A geodesic of a homogeneous Riemannian manifold is called homogeneous if it is an orbit of an one-parameter subgroup of . In the case when is a naturally reductive space, that is the -invariant metric is defined by some non degenerate biinvariant symmetric bilinear form , all geodesics of are homogeneous. We consider the case when is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group , and we give a simple necessary condition that admits a non-naturally...