Showing papers on "Unit tangent bundle published in 1996"
37 citations
TL;DR: In this article, the regularity of weak solutions and the Palais-Smale condition for a functional involving a connection A on a line bundleL and a sectionφ of another bundleW+ constructed from L and a spinor bundle on a given four-dimensional Riemannian manifold were shown.
Abstract: The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection A on a line bundleL and a sectionφ of another bundleW+ constructed fromL and a spinor bundle on a given four-dimensional Riemannian manifold We show the regularity of weak solutions and the Palais-Smale condition for this functional
33 citations
TL;DR: In this article, the authors used the classification of Fano 3-folds to prove that the tangent bundle of an extremal face on a contraction is not stable (i.e. semi-stable or unstable).
Abstract: By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold. Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a contraction $f:X\longrightarrow Y$ of an extremal face on $X$ is a destabilising subsheaf of $T_X$.
26 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
01 Jan 1996
TL;DR: In this article, all natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on a 1-jet bundle are classified. And it is proved that such operators form a 2-parameter family with real coefficients.
Abstract: All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).
25 citations
TL;DR: In this article, the Euler characteristic of the accessible region in configuration space is used to determine the topology of a 3-manifold in a magnetic field for the case of 2-degree-of-freedom Hamiltonian systems.
Abstract: Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if it is not a unit tangent bundle) is uniquely determined by the Euler characteristic of the accessible region in configuration space. In this class of 3-manifolds for most cases there does not
19 citations
TL;DR: In this article, the Euler characteristic of the accessible region in configuration space is used to determine the topology of a 3-manifold in a magnetic field, and it is shown that there are topological obstacles for its existence such that only in the cases of $S 1/times S 2/2$ and $T 2/3$ such a Poincar\'e section can exist.
Abstract: Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if it is not a unit tangent bundle) is uniquely determined by the Euler characteristic of the accessible region in configuration space. In this class of 3-manifolds for most cases there does not exist a transverse and complete Poincar\'e section. We show that there are topological obstacles for its existence such that only in the cases of $S^1\times S^2$ and $T^3$ such a Poincar\'e section can exist.
12 citations
8 citations
Journal Article•
TL;DR: In this article, the authors adopt the methods of pseudohermitian geometry to study the tangent sphere bundle U(M) over a Riemannian manifold M, which is an elliptic space form of sectional curvature 1.
Abstract: We adopt the methods of pseudohermitian geometry (cf. [16]) to study the tangent sphere bundle U(M) over a Riemannian manifold M . If M is an elliptic space form of sectional curvature 1 then U(M) is shown to be globally pseudo-Einstein (in the sense of J. M. Lee, [12]).
8 citations
01 Jan 1996
TL;DR: In this article, the authors give the equations of structure of an N-linear connection in the bundle of accelerations in higher order Lagrange spaces, which correspond to k = 2.
Abstract: The study of higher order Lagrange spaces founded on the notion of bundle of velocities of order k has been recently given by Radu Miron and author in [2]-[5]. The bundle of acceleration correspond in this study to k = 2. In this paper we shall give the equations of structure of an N-linear connection in the bundle of accelerations.
5 citations
Posted Content•
TL;DR: In this paper, the authors translate positivity properties of the tangent bundle (and the anti-canonical bundle) of an algebraic manifold into existence and movability properties of rational curves and investigate the impact on the global geometry of the manifold.
Abstract: The purpose of this paper is to translate positivity properties of the tangent bundle (and the anti-canonical bundle) of an algebraic manifold into existence and movability properties of rational curves and to investigate the impact on the global geometry of the manifold $X$. Among the results we prove are these:
\quad If $X$ is a projective manifold, and ${\cal E} \subset T_X$ is an ample locally free sheaf with $n-2\ge rk {\cal E}\ge n$, then $X \simeq \EP_n$.
\quad Let $X$ be a projective manifold. If $X$ is rationally connected, then there exists a free $T_X$-ample family of (rational) curves. If $X$ admits a free $T_X$-ample family of curves, then $X$ is rationally generated.