Books by Peter B (Univ Of Oregon Gilkey

 This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.

Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. This book presents a comprehensive treatment of various aspects of pseudo-Riemannian geometry.

This work presents results about the geometric consequences that follow if various natural operators defined in terms of the Riemann curvature tensor are assumed to have constant eigenvalues or constant Jordan normal form in the appropriate domains of definition.