Chapter One



Conformal geometry is the study of spaces in which one knows how to measure infinitesimal angles but not lengths. A conformal structure on a manifold is an equivalence class of Riemannian metrics, in which two metrics are identified if one is a positive smooth multiple of the other. The study of conformal geometry has a long and venerable history. From the beginning, conformal geometry has played an important role in physical theories.

A striking historical difference between conformal geometry compared with Riemannian geometry is the scarcity of local invariants in the conformal case. Classically known conformally invariant tensors include the Weyl conformal curvature tensor, which plays the role of the Riemann ...

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