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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7 citations
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TL;DR: In this paper, the authors considered a certain pseudo-Riemannian metric on the tangent bundle of a Riemannians manifold and obtained necessary and sufficient conditions for the pseudoremension to be Ricci flat (see Theorem 2).
Abstract: We consider a certain pseudo-Riemannian metricG on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).
7 citations
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TL;DR: In this paper, a diagonal lift Dg of Riemannian metric g of manifold Mn to the tangent bundle of order two denoted by T2Mn of Mn was defined.
Abstract: In this paper we define a diagonal lift Dg of Riemannian metric g of manifold Mn to the tangent bundle of order two denoted by T2Mn of Mn, we associate to Dg its Levi-civita connection of T2 M and we investigate applications of the diagonal lifts in the killing vectors and geodesics.
7 citations
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TL;DR: The tangent bundle is regarded as an almost product manifold and connections adapted to this structure are introduced in this article, where the theory of submersions is applied to this manifold.
Abstract: The tangent bundle is regarded as an almost product manifold. Connections adapted to this structure are introduced. Use is made of the theory of submersions,
7 citations
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TL;DR: In this paper, the authors determine all Riemannian manifolds for which the tangent sphere bundles, equipped with the Sasaki metric, are local or global product manifolds.
Abstract: We determine all Riemannian manifolds for which the tangent sphere bundles, equipped with the Sasaki metric, are local or global Riemannian product manifolds.
7 citations