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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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08 Nov 2022TL;DR: In this article , the authors studied the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL(2,R), generalizing earlier work of Sarnak and Bourgain-Kontorovich.
Abstract: We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL(2,R), generalizing earlier work of Sarnak and Bourgain-Kontorovich on the growth of the number of reciprocal geodesics on the modular surface. We also prove that reciprocal geodesics are equidistributed in the unit tangent bundle.
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03 Nov 202214 Apr 2023
TL;DR: In this article , the authors study the Riemannian metric bundles and explore their connections with K-theory and other areas of mathematics, such as functional analysis, geometric group theory, and noncommutative geometry.
Abstract: A Riemannian metric bundle G(M) is a fiber bundle over a smooth manifold M, whose fibers are the spaces of symmetric, positive-definite bilinear forms on the tangent spaces of M, which represent the Rieman?nian metrics. In this work, we aim to study the category of Riemannian metric bundles and explore their connections with K-theory and other areas of mathematics. Our main motivation comes from the idea of multi-norms in Banach spaces, which have found applications in di?verse fields such as functional analysis, geometric group theory, and noncommutative geometry. The novelty of our work lies in the rigorous development of the theory of Riemannian metric bundles, and the application of this theory to the study of K-theory and other geometric invariants of manifolds. We hope that our work will contribute to a deeper understanding of the geometry and topology of manifolds equipped with Riemannian metric bundles, and provide new insights into the interplay between geometry, topology, and analysis.
TL;DR: In this article, the authors constructed a metrical structure on the (1, 1)-tensor bundle of a Riemannian manifold equipped with a Cheeger-Gromoll type metric.
Abstract: We construct a metrical framed $$f(3,-1)$$
-structure on the (1, 1)-tensor bundle of a Riemannian manifold equipped with a Cheeger–Gromoll type metric and by restricting this structure to the (1, 1)-tensor sphere bundle, we obtain an almost metrical paracontact structure on the (1, 1)-tensor sphere bundle. Moreover, we show that the (1, 1)-tensor sphere bundles endowed with the induced metric are never space forms.
Posted Content•
06 Sep 2011
TL;DR: In this paper, a generalized Lie algebroid is used to obtain a generalized tangent bundle, and a new class of Lagrange spaces, called by use, generalized Lagrange (ρ, η)-space, Lagrange(ρ, ǫ)space and Finsler (ρ-ǫ)-space are presented.
Abstract: A class of metrizable vector bundles have been presented in the paper [5]. Using a generalized Lie algebroid we obtain the Lie algebroid generalized tangent bundle. This Lie algebroid is a new example of metrizable vector bundle. A new class of Lagrange spaces, called by use, generalized Lagrange (ρ, η)-space, Lagrange (ρ, η)space and Finsler (ρ, η)-space are presented. The results obtained in the particular case of Lie algebroids emphasize the importance and the utility of our new method by work. In particular, if all morphisms are identities morphisms, then similar results with classical results are obtained. 2000 Mathematics Subject Classification:53C05, 53C07, 53C60, 58B20.