The homogeneous geometries of real hyperbolic space
نویسندگان
چکیده
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components. Mathematics Subject Classification (2010). Primary 53C30; Secondary 57S25, 58H15.
منابع مشابه
Limits of Geometries
A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transf...
متن کاملOrbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملAn Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach
The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. In [1], Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the Lorentz group and its underlying hyperbolic geometry. They defined the Chen addition and then Chen model of hyperbolic geomet...
متن کاملOn Rough-isometry Classes of Hilbert Geometries
We prove that Hilbert geometries on uniformly convex Euclidean domains with C 2-boundaries are roughly isometric to the real hyperbolic spaces of corresponding dimension.
متن کاملIsometric Action of Sl2(r) on Homogeneous Spaces
We investigate the SL2(R) invariant geodesic curves with the associated invariant distance function in parabolic geometry. Parabolic geometry naturally occurs in the study of SL2(R) and is placed in between the elliptic and the hyperbolic (also known as the Lobachevsky half-plane and 2dimensional Minkowski space-time) geometries. Initially we attempt to use standard methods of finding geodesics...
متن کامل