Author(s): V N Berestovskii, V V Gorbatsevich
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This paper is a survey of results (partly obtained by the authors) on homogeneous spaces of Lie groups G with a compact stabilizer subgroup H, on which every G-invariant distribution is integrable. It is proved that the condition of integrability is necessary and sufficient for every invariant inner metric to be (holonomic) Finsler on such a space. As a corollary of the obtained results, we assert that the class of homogeneous spaces with invariant non-holonomic Riemannian metrics (in other terms, sub-Riemannian or Carnot–Carathéodory metrics), which were actively studied last 3 decades after Gromov’s work, is rather broad.
This article was published in Analysis and Mathematical Physics
and referenced in Journal of Generalized Lie Theory and Applications