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.

Tangent sphere bundles which are ·¡Einstein

Abstract: We study some almost contact metric structures on the tangent sphere bundles, induced from some almost Hermitian structures of natural diagonal lift type on the tangent bundle of a Riemannian manifold (M;g). The above almost contact metric structures are not automatically contact metric structures. In order to get such properties we made some rescalings of the metric, of the fundamental vector fleld, and of the 1-form. Then we gave the characterization of the Sasakian structures on the tangent sphere bundles. In this case, the base manifold must be of constant sectional curvature. For the obtained Sasakian manifolds we got the condition under which they are · - Einstein.

The vaisman connection on the vertical bundle of a finsler manifold

Abstract: The slit tangent manifold of a Finsler manifold is endowed with two foliations: the vertical foliation and the Liouville foliation, the last being a subfoliation of the first one, [1]. We give an adapted basis on the vertical bundle of such a manifold. In this paper we give the Vaisman connection on the vertical bundle with respect to the Liouville foliation and we compute its coecients with respect to that adapted basis. We prove that the leaves of the vertical foliation are Reinhart spaces.

The Space of (Contact) Anosov Flows on 3-Manifolds

Abstract: The first half of this paper concerns the topology of the space A(M) of (not necessarily contact) Anosov vector fields on the unit tangent bundle M of closed oriented hyperbolic surfaces Σ. We show that there are countably infinite connected components of A(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 forma C 1 -open subset of the space of the Anosov flows which leave a particular C ∞ volume form invariant, if the ambiant manifold is a rational homology sphere.

Second order partial dierential equations (SOPDEs) and nonlinear connections on the tangent bundle of k 1 -velocities of a manifold

Abstract: In this paper I will describe two distinct ways by which it obtain a sequence of SOPDEs and a sequences of nonlinear connections on the tangent bundle of k 1 -velocties T 1 k M, starting from a given SOPDE, follows the ideas of papers (25), (26), (27), (28). Some properties about this sequences is also presented. Interesting cases appear in the presence of a regular Lagrangian on T 1 kM.

Tangent Bundle of the Hypersurfaces in a Euclidean Space

Abstract: We consider an immersed orientable hypersurface f : M ! R n+1 of the Euclidean space (f an immersion), and observe that the tan- gent bundle TM of the hypersurface M is an immersed submanifold of the Euclidean space R 2n+2 . Then we show that in general the induced metric on TM is not a natural metric and obtain expressions for the horizontal and vertical lifts of the vector fields on M. We also study the special case in which the induced metric on TM becomes a natural metric and show that in this case the tangent bundle TM is trivial.