Wednesday, July 4, 2012

1207.0128 (A. Cap et al.)

Einstein metrics in projective geometry    [PDF]

A. Cap, A. R. Gover, H. R. Macbeth
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.
View original:

No comments:

Post a Comment