Ambient construction
From Wikipedia, the free encyclopedia
In conformal geometry, the ambient construction refers to a construction of Charles Fefferman and Robin Graham[1] for which a conformal manifold of dimension n canonically determines a degenerate Riemannian manifold of dimension n+1 (i.e., a null cone) which is realized as the boundary of a pseudo-Riemannian manifold of dimension n+2 up to a certain differential order. The obstruction to embedding for all orders is the obstruction tensor, which is a conformally invariant tensor equal to the Bach tensor in dimension 4. The ambient construction can be used to define a class of conformally invariant differential operators known as the GJMS operators.[2]
A related construction is the tractor bundle.
[edit] See also
[edit] References
- ^ Fefferman, C. and Graham, R. "Conformal invariants", in Élie Cartan et les Mathématiques d'Aujourdui, Asterisque (1985), 95-116.
- ^ Graham, R., Jenne, R., Mason, L.J., and Sparling, G.A.J. "Conformally invarant powers of the Laplacian I: Existence", Jour. Lond. Math. Soc, 46 (1992), 557-565.
 |
This geometry-related article is a stub. You can help Wikipedia by expanding it. |
