Showing papers on "Frame bundle published in 1987"

Varieties in positive characteristic with trivial tangent bundle

Abstract: © Foundation Compositio Mathematica, 1987, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

String quantization on group manifolds and the holomorphic geometry of DiffS1/S1

Abstract: The recent results by Bowick and Rajeev on the relation of the geometry of DiffS1/S1 and string quantization in ℝd are extended to a string moving on a group manifold. A new derivation of the curvature formula (−26/12m3+1/6m)δn, −m for the canonical holomorphic line bundle over DiffS1/S1 is given which clarifies the relation of that bundle with the complex line bundles over infinite-dimensional Grassmannians, studied by Pressley and Segal.

Moduli of Hermite-Einstein Vector Bundles

Abstract: Let M be a compact K/ihler manifold of dimension n with a K/ihler form and let g be a holomorphic vector bundle over M. A Hermitian metric on g gives rise to a natural choice of connection and its curvature is denoted by R. Let K be the contraction of R with respect to the metric 4. Locally, if X1, ..., X, is a unitary frame (for the holomorphic tangent bundle of M) at a point, then K is the mean curvature

Connections on discrete fibre bundles

Abstract: A new approach to gauge fields on a discrete space-time is proposed, in which the fundamental object is a discrete version of a principal fibre bundle. If the bundle is twisted, the gauge fields are topologically non-trivial automatically.

Metrics of negative curvature on vector bundles

Abstract: It is shown that any vector bundle E over a compact base manifold M admits a complete metric of negative (respectively nonpositive) curvature provided M admits a metric of negative (nonpositive) curvature.

On moduli of vector bundles on rational surfaces

Abstract: Let S be a smooth, connected, projective surface (over ~) and H an ample divisor on S. Fix ca ~ Pic (S), c 2 ~ H4(S, ~E) ~ ~E, r 6 Z, r > 1. Let MH(r, c a, c2) be the moduli scheme of H-stable vector bundles of rank r with first Chern class c a and second Chern class c 2 (see [16]). If S = ~2, G. Ellingsrud in [8] proved that Mn (r, ca, c2) is irreducible (if not empty). His construction proved also that Mn (r, Cl, c2) is unirational and for some choice of r, c 1, c 2 even stably rational ([1]). The proofs in [8] are based on [6]. The same methods apply for many other surfaces, in particular for the minimal rational surfaces (see Proposition 2.1). The aim of this paper is to show that this happens (at least for suitable H) for every rational surface. It is natural to ask if this is true for all ample line bundles. For the existence of simple vector bundles on certain rational surfaces, see [2], [19]. In the first version of this paper the main result was stated only for r = 2. The referee remarked that the same proof works in general.

Remarks on the problem of lifting spacetime symmetries

Abstract: The problem of lifting the action of a symmetry group K on spacetime M to automorphisms of a principal bundle P(M, G) is discussed. A classification of bundles P admitting a lift is given for a case more general than that considered by Harnad, Shnider, and Vinet.

Two-plane sub-bundles of nonorientable real vector-bundles

Abstract: Let ζ be a nonorientable m-plane bundle over a CW complex X of dimension m or less Given a 2-plane bundle η over X, we wish to know whether η can be embedded as a sub-bundle of ζ The bundle η need not be orientable When ζ is even-dimensional there is the added complication of twisted coefficients In that case, we use Postnikov decomposition of certain nonsimple fibrations in order to describe the obstructions for the embedding problem Emery Thomas [11] and [12] treated this problem for ζ and η both orientable The results found here are applied to the tangent bundle of a closed, connected, nonorientable smooth manifold, as a special case

Pullbacks of the Horrocks-Mumford bundle.

Abstract: The only known holomorphic rank 2 vector bündle on P\" for n > 4 (except direct sums of line bundles) is the Horrocks-Mumford bündle ^ on P, [H-M], 1973. Of course this is not quite true, since we may twist &* by a line bündle or may pull ̂ back under a finite morphism n: P — > /P. 2F is stable and has Chern-classes ci = — l and c2 = 4 (for a suitable twist). *^ is stable too, cf. [Ba], and has Chern-classes ci(d) = —d and c2(d) = 4d where d is the degree of . Let M(d) = {n: P— > P> of degree d} denote the variety of finite morphisms. Pulling back induces a morphism

On hyper‐relativistic quantum systems

Abstract: A hyper‐relativistic system is defined as one whose equation of motion is form invariant under coordinate transformations induced by a semisimple group whose algebra is contractible to the algebra of the Poincare group. Such a system lies, categorically, in the domain between the special theory of relativity and the general theory, for whereas the former requires covariance under transformations between inertial systems, the latter imposes covariance with respect to arbitrary continuous transformations. In this paper, a new interpretation of a particular fiber‐bundle structure constructed on the timelike homogeneous space M=SO(4,2)/SO(4,1) is presented, and Minkowski space‐time is realized as a subspace of the standard fiber of the tangent bundle over this hyperquadric. Through the process of group contraction, coupled with the commutation of the momentum vector fields with the principal bundle of linear frames with which the tangent bundle is associated, a hierarchy of ‘‘Heisenberg commutation relations,...