Invariant mesures on homogeneous manifolds of reductive type.

Toshiyuki Kobayashi

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A geodesic of a homogeneous Riemannian manifold $(M = G / K, g)$ is called homogeneous if it is an orbit of an one-parameter subgroup of $G$ . In the case when $M = G / H$ is a naturally reductive space, that is the $G$ -invariant metric $g$ is defined by some non degenerate biinvariant symmetric bilinear form $B$ , all geodesics of $M$ are homogeneous. We consider the case when $M = G / K$ is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group $G$ , and we give a simple necessary condition that $M$ admits a non-naturally...

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