The Gauss Map and 2+1 Gravity
arXiv:gr-qc/9403012 · doi:10.1088/0264-9381/11/11/009
Abstract
We prove that the Gauss map of a surface of constant mean curvature embedded in Minkowski space is harmonic. This fact will then be used to study 2+1 gravity for surfaces of genus higher than one. By considering the energy of the Gauss map, a canonical transform between the ADM reduced variables and holonomy variables can be constructed. This allows one to solve (in principle) for the evolution in the ADM variables without having to explicitly solve the constraints first.
Cited by in corpus (7)
- Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
- Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
- Quantum Gravity at Very High Energies
- Constant mean curvature foliations of flat space--times
- Constant mean curvature foliations of simplicial flat spacetimes
- Perturbative Analysis of the Two-body Problem in (2+1)-AdS gravity
- (2+1)-Gravity on Riemann Surfaces in Conformal Gauge