Ambient connections realising conformal Tractor holonomy

Details Ambient connections realising conformal Tractor holonomy Ambient connections realising conformal Tractor holonomy

2006-06-16

arxiv.org/abs/math/0606410v1

Mathematics

Differential Geometry

17 pages

Scientific paper

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal tractor holonomy as affine holonomy of such a connection. We give an example of an ambient connection for which this is the case, and which is torsion free if we start the construction with a C-space, and in addition Ricci-flat if we start with an Einstein manifold. Thus for a $C$-space this example leads to an ambient metric in the weaker sense of \v{C}ap and Gover, and for an Einstein space to a Ricci-flat ambient metric in the sense of Fefferman and Graham.

Affiliated with

Also associated with

No associations

Rating

Ambient connections realising conformal Tractor holonomy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ambient connections realising conformal Tractor holonomy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ambient connections realising conformal Tractor holonomy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-65717