This book contains the proceedings of the Special Session, Geometric Methods in Mathematical Physics, held at the joint AMS-CMS meeting in Vancouver in August 1993. The papers collected here contain a number of new results in differential geometry and its applications to physics. The major themes include black holes, singularities, censorship, the Einstein field equations, geodesics, index theory, submanifolds, CR-structures, and space-time symmetries. In addition, there are papers on Yang-Mills fields, geometric techniques in control theory, and equilibria. Containing new results by established researchers in the field, this book provides a look at developments in this exciting area of research.

Readership

Researchers in differential geometry and mathematical physics.

Table of Contents

• J. K. Beem -- Stability of geodesic incompleteness
• B. K. Berger, D. Garfinkle, V. Moncrief, and C. Swift -- Numerical simulation of two-polarization Gowdy \(T^3\) cosmology
• P. T. Chruściel -- "No hair" theorems--Folklore, conjectures, results
• K. L. Duggal and A. Bejancu -- Spacetime geometry of CR-structures
• P. E. Ehrlich and S.-B. Kim -- From the Riccati inequality to the Raychaudhuri equation
• C. J. Fama and S. M. Scott -- Invariance properties of boundary sets of open embeddings of manifolds and their application to the abstract boundary
• G. J. Galloway -- Least area tori, black holes and topological censorship
• S. G. Harris -- The method of timelike 2-surfaces
• A. D. Helfer -- Conjugate points and higher Arnol'd-Maslov classes
• J. Isenberg and V. Moncrief -- Manifolds with a circle action and the Einstein constraint equations
• W. Israel -- The internal geometry of black holes
• H. P. Künzle -- Einstein-Yang-Mills fields with spherical symmetry
• D. Lewis -- Quasi-periodic motions of planar liquid drops
• P. E. Parker -- Compatible metrics on fiber bundles
• W. F. Shadwick and W. M. Sluis -- Dynamic feedback for classical geometries
• R. Sharma and K. L. Duggal -- Ricci curvature inheriting symmetries of semi-Riemannian manifolds