Geodesic
Canonical representations on two-sheeted hyperboloids
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 91-124 Cet article a éte moissonné depuis la source Math-Net.Ru

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The two-sheeted hyperboloid $\mathcal L$ in $\mathbb R^n$ can be identified with the unit sphere $\Omega$ in $\mathbb R^n$ without the equator. Canonical representations of the group $G=\mathrm{SO}_0(n-1,1)$ on $\mathcal L$ are defined as the restrictions to $G$ of the representations of the overgroup $\widetilde G=\mathrm{SO}_0(n,1)$ associated with a cone. They act on functions and distributions on the sphere $\Omega$. We decompose these canonical representations into irreducible constituents and decompose the Berezin form. 
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V. F. Molchanov. Canonical representations on two-sheeted hyperboloids. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 91-124. http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a7/

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