Rigidity of transformation groups in differential geometry

Abstract

In this survey, symmetry provides a framework for classification of manifolds with differential-geometric structures. We highlight pseudo-Riemannian metrics, conformal structures, and projective structures. A range of techniques have been developed and successfully deployed in this subject, some of them based on algebra and dynamics and some based on analysis. We aim to illustrate this variety.

15 pages, 3 figures; submitted to Notices of the American Mathematical Society; references are limited by the journal; comments welcome