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Orbits of an isotropy subgroup on a pseudo-Riemannian symmetric space of rank 1. (English. Russian original) Zbl 0536.53049
Russ. Math. Surv. 38, No. 5, 158-159 (1983); translation from Usp. Mat. Nauk 38, No. 5(233), 203-204 (1983).
The description of orbits of a connected open subgroup $$H\subset G^{\sigma}\subset G$$ on a pseudo-Riemannian symmetric space G/H of rank 1 is given. Here the subgroup $$G^{\sigma}$$ consists of elements of a real semi-simple Lie group G fixed with respect to the involution $$\sigma$$. The author uses some ideas of T. Oshima and T. Matsaki [J. Math. Soc. Japan 32, 392-414 (1980; Zbl 0451.53039)] who considered the action of H on $$G/G^{\sigma}$$. Additionally, the author considers the averaging of functions from $$C_ 0^{\infty}(G/H)$$ by H and points out the corresponding radial part of the Laplace-Beltrami operator.
Reviewer: B.N.Apanasov
##### MSC:
 53C35 Differential geometry of symmetric spaces 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 57S15 Compact Lie groups of differentiable transformations
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