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The Ambient Metric (AM-178) by C. Robin Graham, Charles Fefferman

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Chapter Two

 

Ambient Metrics

Let M be a smooth manifold of dimension n ≥ 2 equipped with a conformal class [g]. Here, g is a smooth pseudo-Riemannian metric of signature (p, q) on M and [g] consists of all metrics

image

on M, where ϒ is any smooth real-valued function on M.

The space image consists of all pairs (h, x), where x image M, and h is a symmetric bilinear form on TxM satisfying h = s2gx for some . Here and below, gx denotes the symmetric bilinear form ...

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