Local rigidity of 3-dimensional cone-manifolds
نویسندگان
چکیده
منابع مشابه
Local rigidity of 3-dimensional cone-manifolds
We investigate the local deformation space of 3-dimensional conemanifold structures of constant curvature κ ∈ {−1, 0, 1} and coneangles≤ π. Under this assumption on the cone-angles the singular locus will be a trivalent graph. In the hyperbolic and the spherical case our main result is a vanishing theorem for the first Lcohomology group of the smooth part of the cone-manifold with coefficients ...
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We prove global rigidity for compact hyperbolic and spherical cone-3-manifolds with cone-angles ≤ π (which are not Seifert fibered in the spherical case), furthermore for a class of hyperbolic cone-3-manifolds of finite volume with cone-angles ≤ π, possibly with boundary consisting of totally geodesic hyperbolic turnovers. To that end we first generalize the local rigidity result contained in [...
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It is well known that some lattices in SO(n, 1) can be nontrivially deformed when included in SO(n+1, 1) (e.g., via bending on a totally geodesic hypersurface); this contrasts with the (super) rigidity of higher rank lattices. M. Kapovich recently gave the first examples of lattices in SO(3, 1) which are locally rigid in SO(4, 1) by considering closed hyperbolic 3-manifolds obtained by Dehn fil...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2005
ISSN: 0022-040X
DOI: 10.4310/jdg/1143571990