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.
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TL;DR: In this paper, the authors studied the natural almost CR structure on the total space of a subbundle of hyperquadrics of the tangent bundle T(M) over a semi-Riemannian manifold (M, g).
Abstract: We study the natural almost CR structure on the total space of a subbundle of hyperquadrics of the tangent bundle T(M) over a semi-Riemannian manifold (M, g) and show that if the Reeb vector ξ of an almost contact Riemannian manifold is a CR map then the natural almost CR structure on M is strictly pseudoconvex and a posteriori ξ is pseudohermitian. If in addition ξ is geodesic then it is a harmonic vector field. As an other application, we study pseudoharmonic vector fields on a compact strictly pseudoconvex CR manifold M, i.e. unit (with respect to the Webster metric associated with a fixed contact form on M) vector fields X e H(M) whose horizontal lift X↑ to the canonical circle bundle S1 → C(M) → M is a critical point of the Dirichlet energy functional associated to the Fefferman metric (a Lorentz metric on C(M)). We show that the Euler–Lagrange equations satisfied by X↑ project on a nonlinear system of subelliptic PDEs on M.
11 citations
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TL;DR: In this article, it was shown that the geodesic flow on the unit tangent bundle of a hyperbolic orbifold of type 2, q, $\infty$ is left-handed.
Abstract: We establish that, for every hyperbolic orbifold of type (2, q, $\infty$) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of periodic orbits (i) bounds a Birkhoff section for the geodesic flow, and (ii) is a fibered link. We also prove similar results for the torus with any flat metric. Besides, we observe that the natural extension of the conjecture to arbitrary hyperbolic surfaces (with non-trivial homology) is false.
11 citations
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TL;DR: In this article, the rescaled Sasaki metric on a Riemannian manifold was studied and the geodesics on the tangent bundle with respect to the rescaling was investigated.
Abstract: For a Riemannian manifold $M$, we determine some curvature properties of a tangent bundle equipped with the rescaled metric.The main aim of this paper is to give explicit formulae for the rescaled metric on $TM$, and investigate the geodesics on the tangent bundle with respect to the rescaled Sasaki metric.
11 citations
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TL;DR: In this paper, it was shown that when the gerbere presenting a magnetic monopole is viewed as a virtual 2-vector bundle, then it decomposes, modulo torsion, as two times a virtual ς.
Abstract: We show that when the gerberepresenting a magnetic monopole is viewed as a virtual 2-vector bundle, then it decomposes, modulo torsion, as two times a virtual 2-vector bundle ς. We therefore interpret ς as representing half a magnetic monopole, or a semipole.
11 citations