Rigidity of transformation groups in differential geometry

2020/09/29 by Melnick, Karin
#53-02 #Differential Geometry (math.DG) #FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.2009.13937

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.

Related

• Lie Algebras : Classifications, Deformations, Rigidity and Differential Geometry
• Differential geometry of submanifolds of projective space
• Characterizations of model manifolds by means of certain differential systems
• On Gromov's theory of rigid transformation groups: A dual approach
• Quasi-isometric rigidity of three manifold groups