10 citations · 12 across the 7 of their papers we have counts for
7 papers · 1 filter
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…
On the mean curvature of a unit vector field
Alexander Yampolsky
We present an explicit formula for the mean curvature of a unit vector field on a Riemannian manifold, using a special but natural frame. As applications, we treat some known and n…
On the intrinsic geometry of a unit vector field
Alexander Yampolsky
We study the geometrical properties of a unit vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle wit…
Totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold
Alexander Yampolsky
We give a full description of totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold of constant curvature and present a new class of a cylinder-type totall…
Transverse totally geodesic submanifolds of the tangent bundle
Mohamed Tahar Kadaoui Abbassi, Alexander Yampolsky
It is well-known that if is a smooth vector field on a given Riemannian manifold then naturally defines a submanifold transverse to the fibers of the tangent…