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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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TL;DR: In this paper, it was shown that the tangent bundle of the moduli space of stable bundles of rank σ > 2 on a smooth projective curve is always stable, in the sense of Mumford-Takemoto.
Abstract: In this paper, we prove that the tangent bundle of the moduli space $\cSU_C(r,d)$ of stable bundles of rank $r>2$ and of fixed determinant of degree $d$ (such that $(r,d)=1$), on a smooth projective curve $C$ is always stable, in the sense of Mumford-Takemoto. This verifies a well-known conjecture, and is related to a conjectural existence of a Kahler-Einstein metric on Fano varieties with Picard number one.
7 citations
TL;DR: In this paper, it was shown that a compact contact threefold which is bimeromorphically equivalent to a Kaehler manifold and not rationally connected is the projectivised tangent bundle of a kaehler surface.
Abstract: We prove that a compact contact threefold which is bimeromorphically equivalent to a Kaehler manifold and not rationally connected is the projectivised tangent bundle of a Kaehler surface.
7 citations
TL;DR: In this article, it was shown that for any compact Riemann surface C and holomorphic map f : C → M the pullback of the tangent bundle of M is semistable.
Abstract: Let M be a complex projective manifold with the property that for any compact Riemann surface C and holomorphic map f : C → M the pullback of the tangent bundle of M is semistable. We prove that in this case M is a curve or a finite etale quotient of an abelian variety answering a conjecture of Biswas.
7 citations
TL;DR: In this paper, the authors studied the penetration behavior of locally geodesic lines of a pinched negatively curved Riemannian manifold into small neighbourhoods of closed geodesics, and of other compact (locally) convex subsets of M. They gave almost sure Diophantine approximation results of real numbers by quadratic irrationals with respect to general Holder quasi-invariant measures.
Abstract: Let M be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure mF associated with a potential F. We compute the Hausdorff dimension of the conditional measures of mF. We study the mF-almost sure asymptotic penetration behaviour of locally geodesic lines of M into small neighbourhoods of closed geodesics, and of other compact (locally) convex subsets of M. We prove Khintchine-type and logarithm law-type results for the spiraling of geodesic lines around these objects. As an arithmetic consequence, we give almost sure Diophantine approximation results of real numbers by quadratic irrationals with respect to general Holder quasi-invariant measures.
7 citations
Abstract: In the Finsler-spacetime tangent bundle, a simple solution is determined to the torsion relations that were obtained previously to maintain (1) compatibility with Cartan's theory of Finsler space, (2) the almost complex structure, and (3) the vanishing of the covariant derivative of the almost complex structure.
7 citations