Topic
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, it was shown that any second-order dynamic equation on a configuration space X → R of nonrelativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle TX → X of relativisticvelocities.
Abstract: We show that any second-order dynamic equationon a configuration space X → R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX → X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.
2 citations
TL;DR: In this article, the generalized Fermi-Walker transport on the Riemannian tangent bundle has been applied to the composite manifold Lm(Bn) corresponding to infinitesimal polygonal loops in the base space.
2 citations
Posted Content•
TL;DR: In this article, the authors classify smooth locally free actions of the real affine group on closed orientable three-dimensional manifolds up to smooth conjugacy, and show that there exists a non-homogeneous action when the manifold is the unit tangent bundle of a closed surface with a hyperbolic metric.
Abstract: We classify smooth locally free actions of the real affine group on closed orientable three-dimensional manifolds up to smooth conjugacy. As a corollary, there exists a non-homogeneous action when the manifold is the unit tangent bundle of a closed surface with a hyperbolic metric.
2 citations
2 citations
Journal Article•
2 citations