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.

Selfadjoint metrics on almost tangent manifolds whose Riemannian connection is almost tangent

Abstract: Let M be a differentiable manifold of class C ∞, with a given (1, 1) tensor field J of constant rank such that J2=λI (for some real constant λ). J defines a class of conjugate (G-structures on M. For λ>0, one particular representative structure is an almost product structure. Almost complex structure arises when λ<0. If the rank of J is maximum and λ=0, then we obtain an almost tangent structure. In the last two cases the dimension of the manifold is necessarily even. A Riemannian metric S on M is said to be related if one of the conjugate structures defined by S has a common subordinate structure with the G-structure defined by S. It is said to be J-metric if the orthogonal structure defined by S has a common subordinate structure.

On the stability of tangent bundle on double coverings

Abstract: Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let τ: X → Y be a double covering branched along a smooth divisor. We show that IX is stable with respect to τ*H if the tangent bundle IY is semi-stable with respect to some ample line bundle H on Y.

The almost hermitian structures determined by the riemannian structures on the tangent bundle

Abstract: One proves that a Riemannian structure 𝔾 on the total space TM of the tangent bundle (TM, π, M) determines an almost Hermitian structure on TM.

Generalized Cheeger-Gromoll Metrics and the Hopf map

Abstract: We show, using two different approaches, that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on the tangent bundle of a two-sphere, the Hopf map is identified with a Riemannian submersion from the universal covering space of the unit tangent bundle onto the two-sphere. A hyperbolic counterpart dealing with the tangent bundle of a hyperbolic plane is also presented.