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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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25 citations
TL;DR: In this paper, the authors show that if there exists a C 0 conjugacy between the geodesic flows of the unit tangent bundles of M and N, then there exists an isometry G : M → N that induces the same isomorphism as F between the fundamental groups of m and n.
25 citations
TL;DR: In this article, it was shown that the parallel fields are trivial minima for the induced Sasaki metric and that the volume of a vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle.
Abstract: A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.
25 citations
TL;DR: In this article, it was shown that semicalibrated integer multiplicity rectifiable 2-cycles have a unique tangent cone at every point in a Riemannian manifold.
Abstract: Semicalibrated currents in a Riemannian manifold are currents that are calibrated by a comass-1 differential form that is not necessarily closed. This extension of the classical notion of calibrated currents is motivated by important applications in differential geometry such as special Legendrian currents, for example. We prove that semicalibrated integer multiplicity rectifiable 2-cycles have a unique tangent cone at every point. The proof is based on the introduction of a new technique that might be useful for other first-order elliptic problems
25 citations
TL;DR: In this paper, a coordinate-free version of the local classification, due to Walker [Q. J. Math. 1, 69 (1950)], of null parallel distributions on pseudo-Riemannian manifolds is provided.
Abstract: We provide a coordinate-free version of the local classification, due to Walker [Q. J. Math. 1, 69 (1950)], of null parallel distributions on pseudo-Riemannian manifolds. The underlying manifold is realized, locally, as the total space of a fiber bundle, each fiber of which is an affine principal bundle over a pseudo-Riemannian manifold. All structures just named are naturally determined by the distribution and the metric, in contrast with the noncanonical choice of coordinates in the usual formulation of Walker’s theorem.
25 citations