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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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01 Jan 2001
TL;DR: In this paper, the authors derived necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature and gave complete classifications for low dimensions and for conformally flat manifolds.
Abstract: As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.
01 Jan 2002
TL;DR: In this article, the authors consider a product preserving functor F of order r and a connection of order Ron a manifold M. They introduce horizontal lifts of tensor elds and linearconnections from MtoF(M)withrespectto.
Abstract: In this paper we consider a product preserving functor F of order r and a connection of order ron a manifold M. We introduce horizontal lifts of tensor elds and linearconnectionsfrom MtoF(M)withrespectto. Ourdenitionsandresultsgeneralize the particular cases of the tangent bundle and the tangent bundle of higher order.
Posted Content
TL;DR: In this article, it was shown that a complete affine manifold has a partially hyperbolic holonomy group if the tangent bundle pulled over the unit tangent bundles over a sufficiently large compact part splits into expanding, neutral, and contracting subbundles along the geodesic flow.
Abstract: Let $N$ be a complete affine manifold $\mathrm{A}^n/\Gamma$ of dimension $n$ where $\Gamma$ is an affine transformation group and $K(\Gamma, 1)$ is realized as a finite CW-complex. $N$ has a partially hyperbolic holonomy group if the tangent bundle pulled over the unit tangent bundle over a sufficiently large compact part splits into expanding, neutral, and contracting subbundles along the geodesic flow. We will show that the complete affine $n$-manifold has a $P$-Anosov linear holonomy group for a parabolic subgroup $P$ of $GL(n, \mathbf{R})$ if and only if it has a partially hyperbolic linear holonomy group. This will show that if a finitely-presented affine group $\Gamma$ acts on $\mathrm{A}^n$ properly discontinuously and freely with the $k$-Anosov linear group, then $\mathrm{cd}(\Gamma) \leq n-k$. Also, there exists a compact collection of $n-k$-dimensional affine subspaces where $\Gamma$ acts on.
Journal Article
TL;DR: In this paper, a reformulation of the five-dimensional Kaluza-Klein theory is presented, taking into account the fact that these five dimensions of space-time are present on the tangent bundle of the Principal Bundle (B).
Abstract: This paper presents a reformulation of the five-dimensional Kaluza-Klein theory. taking into consideration the fact that these five dimensions of space-time are present on the tangent bundle of the Principal Bundle (B). Tb1s reformulation is possible due to the group U(l) of the fiber which endows B with the structure of a differential manifold. this allowing the reproduction of parallel transport notions on such a manifold. Through this we achieve a criterion to add extra dimensions to the theory. Once this criterion has been established. a metric is constructed on the tangent bundle of B. which is formed by a metric of space-time plus a connection, the a one-form defined in the fiber of B whose curvature 1s proportional to the electromagnetic field. This. the five-dimensional Einstein action is the sum of the four-dimensional Einstein action and the four-dimensional Maxwell action. This formulation yields the Einstein and Maxwell equations, as well as the Yang-Mills equations.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202231
202117
202012
201915
201814