35 research outputs found

    Deforming Euclidean cone 3-manifolds

    Full text link
    Given a closed orientable Euclidean cone 3-manifold C with cone angles less than or equal to pi, and which is not almost product, we describe the space of constant curvature cone structures on C with cone angles less than pi. We establish a regeneration result for such Euclidean cone manifolds into spherical or hyperbolic ones and we also deduce global rigidity for Euclidean cone structures.Comment: Only changes for the grants footnotes have been mad

    The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2Ï€2\pi

    Full text link
    We develop the deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2Ï€2\pi, i.e. contained in the interval (0,2Ï€)(0,2\pi). In the present paper we focus on deformations keeping the topological type of the cone-manifold fixed. We prove local rigidity for such structures. This gives a positive answer to a question of A. Casson.Comment: Minor corrections; references update

    A spinorial energy functional: critical points and gradient flow

    Full text link
    On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor {\phi}. We investigate the basic properties of this functional and study its negative gradient flow, the so-called spinor flow. In particular, we prove short-time existence and uniqueness for this flow.Comment: Small changes, final versio

    A heat flow for special metrics

    Get PDF
    On the space of positive 3–forms on a seven–manifold, we study the negative gradient flow of a natural functional and prove short–time existence and uniqueness

    Local rigidity of 3-dimensional cone-manifolds

    No full text
    We investigate local rigidity of 3-dimensional cone-manifolds with cone-angles not larger than pipi. Under this cone-angle restriction the singular locus is a trivalent graph. We obtain local rigidity in the hyperbolic and the spherical case. From a technical point of view the main result is a vanishing theorem for L2L^2-cohomology of the smooth part of the cone-manifold with coefficients in the flat vectorbundle of infinitesimal isometries. From this local rigidity is deduced by an analysis of the variety of representations.We investigate local rigidity of 3-dimensional cone-manifolds with cone-angles not larger than pipi. Under this cone-angle restriction the singular locus is a trivalent graph. We obtain local rigidity in the hyperbolic and the spherical case. From a technical point of view the main result is a vanishing theorem for L2L^2-cohomology of the smooth part of the cone-manifold with coefficients in the flat vectorbundle of infinitesimal isometries. From this local rigidity is deduced by an analysis of the variety of representations
    corecore