English

Almost conformally Einstein manifolds and obstructions

Differential Geometry 2007-05-23 v1 Mathematical Physics math.MP

Abstract

A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this characterisation leads to a systematic approach to constructing obstructions to conformally Einstein metrics. Relaxing the requirement that the parallel tractor field be generic gives a natural generalisation of the Einstein equations.

Keywords

Cite

@article{arxiv.math/0412393,
  title  = {Almost conformally Einstein manifolds and obstructions},
  author = {A. R. Gover},
  journal= {arXiv preprint arXiv:math/0412393},
  year   = {2007}
}

Comments

proceedings of the 9th International Conference on Differential Geometry and its Applications