In conformal geometry, the ambient construction refers to a construction of Charles Fefferman and Robin Graham for which a conformal manifold of dimension n is realized (ambiently) as the boundary of a certain Poincaré manifold, or alternatively as the celestial sphere of a certain pseudo-Riemannian manifold.
The ambient construction is canonical in the sense that it is performed only using the conformal class of the metric: it is conformally invariant. However, the construction only works asymptotically, up to a certain order of approximation. There is, in general, an obstruction to continuing this extension past the critical order. The obstruction itself is of tensorial character, and is known as the (conformal) obstruction tensor. It is, along with the Weyl tensor, one of the two primitive invariants in conformal differential geometry.
Aside from the obstruction tensor, the ambient construction can be used to define a class of conformally invariant differential operators known as the GJMS operators.
A related construction is the tractor bundle.
Other articles related to "ambient construction, ambient":
... An ambient metric on N~ is a Lorentzian metric h~ such that The metric is homogeneous δω* h~ = ω2 h~ The metric is an ambient extension i* h~ = h, where i* is the pullback along the ... ρ to obtain the asymptotic development of the ambient metric off the null cone ...
Famous quotes containing the word construction:
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (18591952)