Invariant Metrics in Coset Spaces.

Invariant Metrics on G-spaces

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and local...

Projective Invariant Metrics for Einstein Spaces

Holography for Coset Spaces

M/string theory on noncompact, negatively curved, cosets which generalize AdSD+1 = SO(D, 2)/SO(D, 1) is considered. Holographic descriptions in terms of a conformal field theory on the boundary of the spacetime are proposed. Examples include SU(2, 1)/U(2), which is a Euclidean signature (4, 0) space with no supersymmetry, and SO(2, 2)/SO(2) and SO(3, 2)/SO(3), which are Lorentzian signature (4,...

Invariant Metrics and Laplacians on the Siegel-jacobi Spaces

In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.

Constructing Reparameterization Invariant Metrics on Spaces of Plane Curves

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics are characterised by mappings into vector spaces where geodesics can be easily computed. This family consists of Sobolev-type Riemannian metr...