Topic
Unit tangent bundle
About: Unit tangent bundle is a research topic. Over the lifetime, 1056 publications have been published within this topic receiving 15845 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this paper, it was shown that the unit tangent bundle of a Riemannian manifold M equipped with the standard contact metric structure is H-contact if and only if M is 2-stein.
Abstract: A contact metric manifold is said to be H-contact, if its characteristic vector field is harmonic. We prove that the unit tangent bundle of a Riemannian manifold M equipped with the standard contact metric structure is H-contact if and only if M is 2-stein.
4 citations
•
4 citations
•
TL;DR: In this article, a new equation with respect to a unit vector field on Riemannian manifold $M^n$ such that its solution defines a totally geodesic submanifold in the unit tangent bundle with Sasaki metric was presented.
Abstract: We present a new equation with respect to a unit vector field on Riemannian manifold $M^n$ such that its solution defines a totally geodesic submanifold in the unit tangent bundle with Sasaki metric and apply it to some classes of unit vector fields. We introduce a class of covariantly normal unit vector fields and prove that within this class the Hopf vector field is a unique global one with totally geodesic property. For the wider class of geodesic unit vector fields on a sphere we give a new necessary and sufficient condition to generate a totally geodesic submanifold in $T_1S^n$.
4 citations
••
4 citations
••
TL;DR: In this paper, the authors review properties of so-called special conformal Killing tensors on a Rie- mannian manifold and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle TQ.
Abstract: We review properties of so-called special conformal Killing tensors on a Rie- mannian manifold (Q,g) and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle TQ. We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular Lagrangian function E, homo- geneous of degree two in the fibre coordinates on TQ. It is shown that when a symmet- ric type (1,1) tensor field K along the tangent bundle projection : TQ ! Q satisfies a differential condition which is similar to the defining relation of special conformal Killing tensors, there exists a direct recursive scheme again for first integrals of the geodesic spray. Involutivity of such integrals, unfortunately, remains an open problem.
4 citations