Almost conformally Einstein manifolds and obstructions

2004/12/20 by A. R. Gover, Gover, A. R.
Mathematics · Physics and Astronomy · #53A30 #53B20 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53A30 #msc:53B15 #msc:53B20 #secondary 53B15

paper · pdf · doi:10.48550/arxiv.math/0412393

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

arxiv created 2004/12/20 · arxiv updated 2009/12/01

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.

Related

• Obstructions to conformally Einstein metrics in n dimensions
• Almost Einstein and Poincare-Einstein manifolds in Riemannian signature
• Riemannian products which are conformally equivalent to Einstein metrics
• Conformally Kähler structures
• Detecting Einstein geodesics: Einstein metrics in projective and\n conformal geometry