Toward a classification of conformal hypersurface invariants

Investor logo

Warning

This publication doesn't include Faculty of Sports Studies. It includes Faculty of Science. Official publication website can be found on muni.cz.
Authors

BLITZ Samuel Harris

Year of publication 2023
Type Article in Periodical
Magazine / Source Journal of Mathematical Physics
MU Faculty or unit

Faculty of Science

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:

You are running an old browser version. We recommend updating your browser to its latest version.

More info