35 research outputs found
Deforming Euclidean cone 3-manifolds
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
We develop the deformation theory of hyperbolic cone-3-manifolds with
cone-angles less than , i.e. contained in the interval . 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
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
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
We investigate local rigidity of 3-dimensional cone-manifolds with cone-angles not larger than . 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 -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 . 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 -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