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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.
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Posted Content•
TL;DR: In this article, it was shown that every geodesic flow on the unit tangent bundle of a negatively curved 2-dimensional orbifold is almost equivalent to the suspension of some automorphism of the torus.
Abstract: Two flows on two compact manifolds are almost equivalent if there is a homeomorphism from the complement of a finite number of periodic orbits of the first flow to the complement of the same number of periodic orbits of the second flow that sends orbits onto orbits. We prove that every geodesic flow on the unit tangent bundle of a negatively curved 2-dimensional orbifold is almost equivalent to the suspension of some automorphism of the torus. Together with a result of Minikawa, this implies that all algebraic Anosov flows are pairwise almost equivalent. We initiate the study of the Ghys graph ---an analogue of the Gordian graph in this context-by giving explicit upper bounds on the distances between these flows.
1 citations
Journal Article•
TL;DR: In this paper, the authors studied a class of contact metrics with compatible almost complex structures on the tangent bundle TM of a Riemannian manifold, which are parallel to those in [10].
Abstract: In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle TM of a Riemannian manifold (M,g), which are parallel to those in [10]. These metrics generalize the classical Sasaki metric and Cheeger-Gromoll metric. We prove that the tangent bundle TM endowed with each pair of the above metrics and the corresponding almost complex structures is a locally conformal almost K¨ahler manifold. We also find that, when restricted to the unit tangent sphere bundle, these metrics and corresponding almost complex structures define new examples of contact metric structures.
1 citations
30 Jun 2020
TL;DR: In this paper, natural paracontact magnetic trajectories in the unit tangent bundle are characterized as those satisfying a certain conservation law, i.e., those that are associated to g-natural paracctact metric structures.
Abstract: In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, ie, those that are associated to g-natural paracontact metric structures We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics)
1 citations
Posted Content•
TL;DR: The main purpose of as discussed by the authors is to investigate the Killing vector field on the tangent bundle of the Riemannian manifold with respect to the Levi-Civita connection of the metric II+III.
Abstract: The main purpose of the paper is to investigate Killing vector field on the tangent bundle T(M_{n}) of the Riemannian manifold with respect to the Levi-Civita connection of the metric II+III .
1 citations
TL;DR: In this paper, a simple correspondence between the geodesics in a tangent bundle and the path of a spinning particle in curved spacetime is presented, where the path is described as a straight line.
1 citations