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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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TL;DR: In this paper, the authors studied non-Kahler manifold with trivial logarithmic tangent bundle and showed that each such manifold arises as a fibre bundle with a compact complex parallelizable manifold as basis and a compactficiation of a semi-torus as fibre.
Abstract: We study non-Kahler manifolds with trivial logarithmic tangent bundle. We show that each such manifold arises as a fibre bundle with a compact complex parallelizable manifold as basis and a compactficiation of a semi-torus as fibre.
5 citations
TL;DR: In this article, the authors prove finiteness results for the class ℳa,b,π,n of n-manifolds that have fundamental groups isomorphic to π and that can be given complete Riemannian metrics of sectional curvatures within {a, b} where a≤b < 0.
Abstract: We prove several finiteness results for the class ℳa,b,π,n of n-manifolds that have fundamental groups isomorphic to π and that can be given complete Riemannian metrics of sectional curvatures within {a,b} where a≤b<0. In particular, if M is a closed negatively curved manifold of dimension at least three, then only finitely many manifolds in the class ℳa,b,π1(M),n are total spaces of vector bundles over M. Furthermore, given a word-hyperbolic group π and an integer n there exists a positive e=e(n,π) such that the tangent bundle of any manifold in the class ℳ-1-e, -1, π, n has
zero rational Pontrjagin classes.
5 citations
5 citations
TL;DR: In this article, a rigid 4-dimensional body Θ with mass m and smooth 3-dimensional boundary ∂Θ has inertia tensor of the form diag{I1, I2, I2, I 2, I 2} in some coordinate system Dx1x2x3x4 attached to Θ and the distance from the point D to the point N of application of a force S is a function depending on at least a certain angle α.
Abstract: Suppose that a rigid 4-dimensional body Θ with mass m and smooth 3-dimensional boundary ∂Θ has inertia tensor of the form diag{I1, I2, I2, I2} in some coordinate system Dx1x2x3x4 attached to Θ. The distance from the point D to the point N of application of a force S is a function depending on at least a certain angle α: DN = R(α, . . .) (cf. [1]–[3]). The force S has magnitude S = s(α) sgn cos α · v, |vD| = v, where s is a function characterizing both the energy dissipation and the energy pumping in the system [1], [2]. Here we take S = Sv(α) = Bv cos α, where B > 0. If Ω ∈ so(4) is the angular velocity tensor of Θ, then the part of the equations of motion corresponding to the Lie algebra so(4) has the following form [2]:
5 citations
27 Aug 2009
TL;DR: In this paper, the relation between the Lie algebra of the infinitesimal fibre-preserving conformal transformations of the tangent bundle of a Riemannian manifold with respect to the synectic lift of the metric tensor is investigated.
Abstract: The purpose of the present article is to investigate some relations between the Lie algebra of the infinitesimal fibre-preserving conformal transformations of the tangent bundle of a Riemannian manifold with respect to the synectic lift of the metric tensor and the Lie algebra of infinitesimal projective transformations of the Riemannian manifold itself.
5 citations