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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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