Einstein metrics in projective geometry
Differential Geometry
2015-09-29 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first BGG equation. The general theory of such equations singles out a subclass of so-called normal solutions. We prove that non-degerate normal solutions are equivalent to pseudo-Riemannian Einstein metrics in the projective class and observe that this connects to natural projective extensions of the Einstein condition.
Cite
@article{arxiv.1207.0128,
title = {Einstein metrics in projective geometry},
author = {A. Cap and A. R. Gover and H. R. Macbeth},
journal= {arXiv preprint arXiv:1207.0128},
year = {2015}
}
Comments
10 pages. Adapted to published version. In addition corrected a minor sign error