Extended obstruction tensors and renormalized volume coefficients

By Robin Graham. 2008

51 citations recorded by the source corpus.

Abstract The behavior is investigated of the renormalized volume coefficients associated to a pseudo-Riemannian metric under conformal change of the metric. It is shown that the renormalized volume coefficients define second order fully nonlinear operators in the conformal factor whose algebraic structure is elucidated via the introduction of “extended obstruction tensors”. These together with the Schouten tensor constitute building blocks for the coefficients in the ambient metric expansion. The renormalized volume coefficients have recently been considered by Chang and Fang motivated by comparison with the elementary symmetric functions of the eigenvalues of the Schouten tensor.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f9f126eb407e9d5686391ca3510108ed735d5815