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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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30 Oct 2015
TL;DR: In this article, a special family of metrics which rescale the horizontal part by a nonzero differentiable function on the tangent bundle over a Riemannian manifold is defined.
Abstract: In this paper, we define a special new family of metrics which rescale the horizontal part by a nonzero differentiable function on the tangent bundle over a Riemannian manifold. We investigate curvature properties of the Levi-Civita connection and another metric connection of the new Riemannian metric.
2 citations
Journal Article•
TL;DR: Tangent sphere bundles of constant holomorphic sectional curvature or of constant?-sectional curvature are classified in this article, and the Hypersurface geometry of tangent spheres is developed.
Abstract: This paper has two purposes. (1) Holomorphic sectional curvature and ?-sectional curvature of tangent sphere bundles are investigated. In particular, tangent sphere bundles of constant holomorphic sectional curvature or of constant ?-sectional curvature are classified. (2) Hypersurface geometry of tangent sphere bundles is developed. Tangent sphere bundles with pseudo-parallel shape operator or ?-parallel shape operator are classified
2 citations
TL;DR: In this paper, it was shown that a class of regular centers, so that quasi-smoothness is preserved by blowing-up, can be enlarged and characterized by means of their jacobian ideal and some geometrical conditions.
Abstract: We study a notion of quasi-smoothness which makes possible to associate a canonical tangent bundle to certain arithmetical schemes (see [V1]). In this context we prove that we can associate a jacobian ideal to any irreducible subscheme. A class of regular centers, so that quasi-smoothness is preserved by blowing-up, will be enlarged and characterized by means of their jacobian ideal and some geometrical conditions, improving the results appearing in [V1].
2 citations
TL;DR: In this paper, the singularities of the quadratic forms on a manifold are described in a generic context and their geometric and algebraic properties are studied, using these results, they treat the problem whether there are Lagrangians on the tangent bundle of a manifold that define a Lagrangian vector field everywhere on the manifold, despite the fact that their Legendre transformation is singular, and the projection of its integral curves gives the solutions of the corresponding variational problem.
2 citations
Journal Article•
TL;DR: In this paper, the authors apply a result of Nagano to prove that an integrable almost tangent manifold M endowed with a vector field satisfying similar properties to those satisfied by the canonical vector field of a vector bundle admits a unique vector bundle structure such that M is isomorphic to a tangent bundle.
Abstract: We apply a result of Nagano to prove that an integrable almost tangent manifold M endowed with a vector field satisfying similar properties to those satisfied by the canonical vector field of a vector bundle admits a unique vector bundle structure such that M is isomorphic to a tangent bundle. Thus we obtain a characterization of tangent bundles. This characterization was obtained by Crampin et al. and Filippo et al. in a different way. We also extend the result to stable tangent bundles. An application to reduction of degenerate autonomous and non-autonomous Lagrangian systems is given.
2 citations