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.

Which geodesic flows are left-handed ?

Abstract: We prove that the geodesic flow on the unit tangent bundle to a hyperbolic 2-orbifold is left-handed if and only if the orbifold is a sphere with three conic points As a consequence, on the unit tangent bundle to a 3-conic sphere, the lift of every finite collection of closed geodesics that is zero in integral homology is the binding of an open book decomposition

g-Natural metrics of constant sectional curvature

Abstract: We prove that the tangent bundle endowed with a g-natural metrics has constant sectional curvature if and only if it is flat, and then we give a characterization of flat g-natural metrics on tangent bundles

Almost-contact structures on hypersurfaces of the tangent bundle of a Riemannian manifold

Abstract: Twenty years ago the systematic investigation of almost-contact structures, i.e., (% ~,~)structures began [4]. First global questions, questions of existence were considered, later their properties were studied: normality, integrability, being contact, etc. In 1967, the investigation of hyperbolic analogs of almost-contact structures began [2]. These structures arise in geometry just as naturally as almost-contact structures (of elliptic type): if a (~ ~,~) -structure arises on hypersurfaces of an almost-complex manifold, then an almost -~ contact structure of hyperbolic type arises on hypersurfaces of an almost-double manifold, When an A-metric of B-metrlc is given on an almost-complex or almost-double manifold, on a hypersurface there arises an almost-contact metric structure (% 4, ~, g) of elliptic or hyperbolic type of the first or second kind, respectively [2].

Conformally flat tangent bundles with general natural lifted metrics

Abstract: We study the conditions under which the tangent bundle $(TM,G)$ of an $n$-dimensional Riemannian manifold $(M,g)$ is conformally flat, where $G$ is a general natural lifted metric of $g$ We prove that the base manifold must have constant sectional curvature and we find some expressions for the natural lifted metric $G$, such that the tangent bundle $(TM,G)$ become conformally flat

The space of (contact) Anosov flows on 3-manifolds

Abstract: The first half of this paper is concerned with the topology of the space $\AAA(M)$ of (not necessarily contact) Anosov vector fields on the unit tangent bundle $M$ of closed oriented hyperbolic surfaces $\Sigma$. We show that there are countably infinite connected components of $\AAA(M)$, each of which is not simply connected. In the second part, we study contact Anosov flows. We show in particular that the time changes of contact Anosov flows form a $C^1$-open subset of the space of the Anosov flows which leave a particular $C^\infty$ volume form invariant, if the ambiant manifold is a rational homology sphere.