Pseudo-Riemannian Homogeneous Structures

This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures, an essential tool in the study of pseudo-Riemannian homogeneous spaces. Benefiting from large symmetry groups, these spaces are of high interest in Geometry and Theoretical Physics.Since the seminal book by Tricerri and Vanhecke, the theory of homogeneous structures has been considerably developed and many applications have been found. The present work covers a gap in the literature of more than 35 years, presenting the latest contributions to the field in a modern geometric approach, with special focus on manifolds equipped with pseudo-Riemannian metrics.This unique reference on the topic will be of interest to researchers working in areas of mathematics where homogeneous spaces play an important role, such as Differential Geometry, Global Analysis, General Relativity, and Particle Physics.

1 G-structures, holonomy and homogeneous spaces.- 2 Ambrose-Singer connections and homogeneous spaces.- 3 Locally homogeneous pseudo-Riemannian manifolds.- 4 Classification of homogeneous structures.- 5 Homogeneous structures of linear type.- 6 Reduction of homogeneous structures.- 7 Where all this fails: non-reductive homogeneous pseudo-Riemannian manifolds.- Subject Index