10 citations · 14 across the 11 of their papers we have counts for
11 papers
Caustics of wave fronts reflected by a surface
Alexander Yampolsky, Oleksandr Fursenko
One can often see caustic by reflection in nature, but it is rather hard to understand the way of how caustic arise and which geometric properties of a mirror surface define the ge…
Minimal unit vector fields on oscillator groups
Alexander Yampolsky
In this paper, we treat minimal left-invariant unit vector fields on oscillator group and their relations with the ones that define a harmonic map. Particularly, if all structure c…
On geodesics of Berger tangent sphere bundle of Hermitian locally symmetric manifold
Alexander Yampolsky
We propose a special deformation of the Sasaki metric on tangent and unit tangent bundle of a Hermitian locally symmetric manifold. Geodesics of this deformed metric have different…
Invariant totally geodesic unit vector fields on three-dimensional Lie groups
Alexander Yampolsky
We give a complete list of those left invariant unit vector fields on three-dimensional Lie groups with the left-invariant metric that generate a totally geodesic submanifold in th…
Totally geodesic property of the Hopf vector field
A. Yampolsky
We prove that the Hopf vector field is a unique one among geodesic covariantly normal unit vector fields on spheres such that the submanifold generated by the field is totally geod…
Powers of the space forms curvature operator and geodesics of the tangent bundle
Yelena Saharova, Alexander Yampolsky
It is well-known that if a curve is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold then the projected curve has all it…