scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Posted ContentDOI
06 Nov 2022
TL;DR: In this article , it was shown that the existence of a logarithmic connection on a principal bundle over a toric variety, singular along the boundary divisor, is equivalent to a torus equivariant structure on the bundle.
Abstract: Let $X$ be a normal projective variety over an algebraically closed field of characteristic zero. Let $D$ be a reduced Weil divisor on $X$. Let $G$ be a reductive linear algebraic group. We introduce the notion of a logarithmic connection on a principal $G$-bundle over $X$, which is singular along $D$. The existence of a logarithmic connection on the frame bundle associated with a vector bundle over $X$ is shown to be equivalent to the existence of a logarithmic covariant derivative on the vector bundle if the logarithmic tangent sheaf of $X$ is locally free. Additionally, when the algebraic group $G$ is semisimple, we show that a principal $G$-bundle admits a logarithmic connection if and only if the associated adjoint bundle admits one. We also prove that the existence of a logarithmic connection on a principal bundle over a toric variety, singular along the boundary divisor, is equivalent to the existence of a torus equivariant structure on the bundle.
Journal ArticleDOI
TL;DR: In this article, the authors considered the associated bundle ξ = (G × KG/K, ρξ, G/k, G k, G m, G n, G rm) and the tangent bundle τG/k = (TG/m, πG/M, G g m, Rm), and gave special examples of odd dimensional solvable Lie groups equipped with left invariant Riemannian metric, and proved some conditions about existence of homogeneous geodesic vectors on the fiber space of ξ and τ
Abstract: The paper considers the associated bundle ξ = (G × KG/K, ρξ, G/K, G/K) and the tangent bundle τG/K = (TG/K, πG/K, G/K, Rm), and gives special examples of odd dimensional solvable Lie groups equipped with left invariant Riemannian metric. Some conditions about existence of homogeneous geodesic vectors on the fiber space of ξ and τG/K are proved.
Journal ArticleDOI
TL;DR: In this paper, the second order almost transverse structure of a differential manifold is defined and conditions for it to admit a real almost product and a generalised almost tangent structure of second order.
Abstract: The present work is based on a type of structures on a differential manifold $V$, called $G$-structures of the second kind, defined by endomorphism $J$ on the second order tangent bundle $T^2(V)$. Our objective is to give conditions for a differential manifold to admit a real almost product and a generalised almost tangent structure of second order. The concepts of the second order frame bundle $H^2(V)$, its structural group $L^2$ and its associated tangent bundle of second order $T^2(V)$ of a differentiable manifold $V$, are used from the point of view that is described in papers \cite{5} and \cite{6}. Also, the almost tangent structure of order two is mentioned and its generalisation, the second order almost transverse structure, is defined.
Journal ArticleDOI
TL;DR: In this paper, the authors investigated the distribution of orbits of a non-elementary discrete hyperbolic subgroup Γ acting on ℍn and its geometric boundary.
Abstract: We investigate the distribution of orbits of a non-elementary discrete hyperbolic subgroup Γ acting on ℍn and its geometric boundary ∂∞(ℍn). In particular, we show that if Γ admits a finite Bowen–Margulis–Sullivan measure (for instance, if Γ is geometrically finite), then every Γ-orbit in ∂∞(ℍn) is equidistributed with respect to the Patterson–Sullivan measure supported on the limit set Λ(Γ). The appendix by Maucourant is the extension of a part of his PhD thesis where he obtains the same result as a simple application of Roblin’s theorem. Our approach is via establishing the equidistribution of solvable flows on the unit tangent bundle of Γ∖ℍn, which is of independent interest.
Posted Content
TL;DR: In this article, a non-linear heat flow corresponding to the almost Hermitian-Einstein equation introduced by N.C. Leung was constructed, and a potential function for this flow was shown to decrease along the flow.
Abstract: Let $X$ be a compact Kahler manifold, $E\to X$ a Hermitian vector bundle and $L\to X$ an ample line bundle. We construct a non-linear heat flow corresponding to the almost Hermitian-Einstein equation introduced by N.C. Leung, and prove that the solution exists for a short time. We also construct a potential function $D_k$ for this flow. In particular, $D_k$ decreases along the flow.

Network Information
Related Topics (5)
Cohomology
21.5K papers, 389.8K citations
90% related
Manifold
18.7K papers, 362.8K citations
89% related
Lie group
18.3K papers, 381K citations
88% related
Symplectic geometry
18.2K papers, 363K citations
88% related
Moduli space
15.9K papers, 410.7K citations
87% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202231
202117
202012
201915
201814