In this chapter we study conformal curvature tensors of a pseudo-Riemannian metric *g*. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to *g*. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group *O*(*p* + 1, *q* + 1) on tensors. We assume throughout this chapter that *n* ≥ 3.

Let *g* be a metric on a manifold *M*. By Theorem 2.9, there is an ambient metric in normal form relative to *g*, which by Proposition 2.6 we may take to be straight. Such a metric takes the form (3.14) on a neighborhood of × *M* × {0} in × *M* × . Equations (3.17) determine the 1-parameter family of metrics ...

Start Free Trial

No credit card required