Toward a classification of conformal hypersurface invariants
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1063/5.0147870 |
| Doi | http://dx.doi.org/10.1063/5.0147870 |
| Keywords | General relativity; Anti-de Sitter space; Differentiable manifold; Differential geometry; Tensor formalism; Riemannian geometry |
| Description | Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a Riemannian (or Lorentzian) conformal manifold. We construct a finite and minimal family of hypersurface tensors-the curvatures intrinsic to the hypersurface and the so-called "conformal fundamental forms"-that can be used to construct natural conformal invariants of the hypersurface embedding up to a fixed order in hypersurface-orthogonal derivatives of the bulk metric. We thus show that these conformal fundamental forms capture the extrinsic embedding data of a conformal infinity in a spacetime. |
| Related projects: |