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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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2 citations
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TL;DR: In this paper, a foliation is said to be transversally tangent if the jacobian matrices of the change of the transverse coordinates are in the tangent group.
Abstract: A foliation ℱ on a differentiable manifold M is said to be transversally tangent if the jacobian matrices of the change of the transverse coordinates are in the tangent group. Such foliation exists if and only if there is an endomorphism J of its normal bundle such that J2=0 and such that the Nijenhuis tensor of J is the zero-tensor. In the special case of the tangent bundle of order 2, T2M, its total space has a natural (1, 1)-tensor F such that F3=0 and an integrable almost-tangent structure. We study several Lie algebras associated to these structures.
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TL;DR: An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(ℝ).
Abstract: An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(ℝ). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant distribution on a closed hyperbolic surface is obtained.
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20 Aug 2008
TL;DR: The complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces was proved in this article, where it was shown that if the global holomorphic sections of tangent bundle generate each fibre, then $M$ is a complex homogeneous manifold.
Abstract: Let $M$ be a close complex manifold and $TM$ its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then $M$ is a complex homogeneous manifold. Our proof depends on the complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces.
2 citations
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2 citations