Algebras of invariant differential operators on unit sphere bundles over two-point homogeneous Riemannian spaces

Abstract

Let $G$ be the identity component of the isometry group for an arbitrary curved two-point homogeneous space $M$. We consider algebras of $G$-invariant differential operators on bundles of unit spheres over $M$. The generators of this algebra and the corresponding relations for them are found. The connection of these generators with two-body problem on two-point homogeneous spaces is discussed.

LaTeX, 38 pages, 1 figure, octonionic case was included in the 3-rd version, some errors were corrected in the 4-th one

Cited by in corpus (1)

• Two-body quantum mechanical problem on spheres