Publication details

Toward a classification of conformal hypersurface invariants

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BLITZ Samuel Harris

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

Faculty of Science

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.
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