Showing papers on "Unit tangent bundle published in 1987"
TL;DR: In this paper, it was shown that any measure-theoretic conjugacy (h, μ) → (h′, μ′) is a C1 diffeomorphism, where h is a uniformly parametrized flow along the horocycle foliation and μ is a measure of maximal entropy.
Abstract: Let g be the geodesic flow on the unit tangent bundle of a C3 compact surface of negative curvature. Let μ be the g-invariant measure of maximal entropy. Let h be a uniformly parametrized flow along the horocycle foliation, i.e., such a flow exists, leaves μ invariant, and is unique up to constant scaling of the parameter (Margulis). We show that any measure-theoretic conjugacy: (h, μ) → (h′, μ′) is a.e. of the form θ, where θ is a homeomorphic conjugacy: g → g′. Furthermore, any homeomorphic conjugacy g → g′; must be a C1 diffeomorphism.
50 citations
TL;DR: In this paper, an almost tangent structure on a tangent bundle is defined on jet bundles of a fibred manifold, which is used to construct a Cartan form for first-order Lagrangians.
Abstract: An operator analogous to the almost tangent structure on a tangent bundle is defined on jet bundles of a fibred manifold. This operator is used to construct a Cartan form. The construction is unique for first-order Lagrangians and is also unique when restricted to higher-order mechanics.
49 citations
TL;DR: In this paper, it was shown that the cotangent bundle T ∗ T M of the tangent bundle of any differentiable manifold M carries an integrable almost tangent structure which is generated by a natural lifting procedure from the canonical almost-tent structure (vertical endomorphism) of T M.
17 citations
TL;DR: In this paper, the tangent bundle of a closed, connected, non-orientable smooth manifold is embedded as a sub-bundle of a 2-plane bundle over a CW complex of dimension m or less.
Abstract: Let ζ be a nonorientable m-plane bundle over a CW complex X of dimension m or less Given a 2-plane bundle η over X, we wish to know whether η can be embedded as a sub-bundle of ζ The bundle η need not be orientable When ζ is even-dimensional there is the added complication of twisted coefficients In that case, we use Postnikov decomposition of certain nonsimple fibrations in order to describe the obstructions for the embedding problem Emery Thomas [11] and [12] treated this problem for ζ and η both orientable The results found here are applied to the tangent bundle of a closed, connected, nonorientable smooth manifold, as a special case
6 citations
5 citations
2 citations
Journal Article•
1 citations
TL;DR: In this paper, a new interpretation of a particular fiber-bundle structure constructed on the timelike homogeneous space M=SO(4,2)/SO (4,1) is presented, and Minkowski space-time is realized as a subspace of the standard fiber of the tangent bundle over this hyperquadric.
Abstract: A hyper‐relativistic system is defined as one whose equation of motion is form invariant under coordinate transformations induced by a semisimple group whose algebra is contractible to the algebra of the Poincare group. Such a system lies, categorically, in the domain between the special theory of relativity and the general theory, for whereas the former requires covariance under transformations between inertial systems, the latter imposes covariance with respect to arbitrary continuous transformations. In this paper, a new interpretation of a particular fiber‐bundle structure constructed on the timelike homogeneous space M=SO(4,2)/SO(4,1) is presented, and Minkowski space‐time is realized as a subspace of the standard fiber of the tangent bundle over this hyperquadric. Through the process of group contraction, coupled with the commutation of the momentum vector fields with the principal bundle of linear frames with which the tangent bundle is associated, a hierarchy of ‘‘Heisenberg commutation relations,...
1 citations