Geometric Space–Frequency Analysis on Manifolds

Geometric structures on manifolds

This document is a sample prepared to illustrate the use of the American Mathematical Society’s LTEX document class amsbook and publication-specific variants of that class.

Geometric symmetries on Lorentzian manifolds

Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used not only to find new solutions of Einstein’s field equations but to classify the spaces also. Different classification schemes are presented here. Relations...

Geometric structures on 3–manifolds

Analysis of Geometric Operators on Open Manifolds: a Groupoid Approach

The first five sections of this paper are a survey of algebras of pseudodifferential operators on groupoids. We thus review differentiable groupoids, the definition of pseudodifferential operators on groupoids, and some of their properties. We use then this background material to establish a few new results on these algebras that are useful for the analysis of geometric operators on non-compact...

Geometric connections and geometric Dirac operators on contact manifolds

We construct some natural metric connections on metric contact manifolds compatible with the contact structure and characterized by the Dirac operators they determine. In the case of CR manifolds these are invariants of a fixed pseudo-hermitian structure, and one of them coincides with the Tanaka–Webster connection.  2005 Elsevier B.V. All rights reserved. MSC: 53B05; 53C15; 53D10; 53D15