Almost conformally Einstein manifolds and obstructions
微分几何
2007-05-23 v1 数学物理
math.MP
摘要
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.
引用
@article{arxiv.math/0412393,
title = {Almost conformally Einstein manifolds and obstructions},
author = {A. R. Gover},
journal= {arXiv preprint arXiv:math/0412393},
year = {2007}
}
备注
proceedings of the 9th International Conference on Differential Geometry and its Applications