26 citations · 50 across the 7 of their papers we have counts for
7 papers
Nonintegrability of the two-body problem in constant curvature spaces II
Alexey V. Shchepetilov
We consider the reduced two-body problem with a central potential on the sphere and the hyperbolic plane . For two potentials different from the Newton a…
Nonintegrability of the two-body problem in constant curvature spaces
Alexey V. Shchepetilov
We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere and the hyperbolic plane . For both types of interac…
Two-body quantum mechanical problem on spheres
Alexey V. Shchepetilov
The quantum mechanical two-body problem with a central interaction on the sphere is considered. Using recent results in representation theory an ordinary differential…
Two-body problem on spaces of constant curvature
A. V. Shchepetilov, I. E. Stepanova
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-b…
The geometric sense of R. Sasaki connection
Alexey V. Shchepetilov
For the Riemannian manifold two special connections on the sum of the tangent bundle and the trivial one-dimensional bundle are constructed. These connections are…
Algebras of invariant differential operators on unit sphere bundles over two-point homogeneous Riemannian spaces
Alexey V. Shchepetilov
Let be the identity component of the isometry group for an arbitrary curved two-point homogeneous space . We consider algebras of -invariant differential operators on bun…