tangent bundle


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tangent bundle

[′tan·jənt ‚bənd·əl]
(mathematics)
The fiber bundle T (M) associated to a differentiable manifold M which is composed of the points of M together with all their tangent vectors. Also known as tangent space.
References in periodicals archive ?
Some substantially revised from the presentations, 22 papers discuss such topics as exact solutions to a Muskat problem with line distributions of sinks and sources, some inequalities for holomorphic self-maps of the unit disc with two fixed points, elliptic perturbations of dynamical systems with a proper node, a porosity theorem for a class of non-expansive set-valued mappings, and a shadow problem for the tangent bundle of straight lines on a sphere.
A Riemannian metric on M is bundle-like if the leaves of the foliation F are locally equidistant, that is, the metric g on M induces a holonomy invariant transverse metric on the normal bundle Q = TM/TF where TF is the tangent bundle of F.
My plan is to combine powerful recent results obtained on the duality of positive cohomology cones with an analysis of the instability of the tangent bundle, i.
This implies that the tangent bundle forms an isomorphic group to ([R.
In fact, he solved the Hartshorne conjecture, which says that the projective space is the only projective manifold with ample tangent bundle [12].
Fano manifolds with nef tangent bundle and large Picard number Kiwamu WATANABE Communicated by Shigefumi MORI, M.
M] and its submanifold M by the same letter g, TM is the tangent bundle of M, and [T.
n] is a smooth, real, n--dimensional manifold M equipped with a so-called regular differentiable Lagrangian: a mapping on the total space TM of tangent bundle (TM, [pi],M): L : [?
A Finsler manifold M has a tangent bundle [pi]: TM [right arrow] M.
Contributors address such topics as two curvature-driven problems in Riemann-Finsler geometry, curvature properties of certain metrics, a connectiveness principle in positively curved Finsler manifolds, Riemann-Finsler surfaces, Finsler geometry in the tangent bundle, and topics in Finsler-inspired differential geometry such as perturbations of constant connection Wagner spaces, path geometries of almost-Grassmann structures, Ehresmann connections in relation to metrics and good metric derivatives and dynamical systems of the Lagrangian and Hamiltonian mechanical systems.
The flag space of the classical Mobius plane can also be obtained by taking the tangent bundle of [S.