Differential Geometry and Relativity : A Volume in Honour of André Lichnerowicz on His 60th Birthday

On the occasion of the sixtieth birthday of Andre Lichnerowicz a number of his friends, many of whom have been his students or coworkers, decided to celebrate this event by preparing a jubilee volume of contributed articles in the two main fields of research marked by Lichnerowicz's work, namely differential geometry and mathematical physics. Limitations of space and time did not enable us to include papers from all Lichnerowicz's friends nor from all his former students. It was equally impossible to reflect in a single book the great variety of subjects tackled by Lichnerowicz. In spite of these limitations, we hope that this book reflects some of the present trends of fields in which he worked, and some of the subjects to which he contributed in his long - and not yet finished - career. This career was very much marked by the influence of his masters, Elie Cartan who introduced him to research in mathematics, mainly in geometry and its relations with mathematical physics, and Georges Darmois who developed his interest for mechanics and physics, especially the theory of relativity and electromagnetism. This par­ ticular combination, and his personal talent, made of him a natural scientific heir and continuator of the French mathematical physics school in the tradition of Henri Poincare. Some of his works would even be best qualified by a new field name, that of physical ma­ thematics: branches of pure mathematics entirely motivated by physics. Front Matter....Pages I-XI Thirty Years of Activity in the Renovation of Mathematical Education....Pages 1-2 Front Matter....Pages 3-3 The Scalar Curvature....Pages 5-18 On Automorphisms of Spaces of Nonpositive Curvature with Finite Volume....Pages 19-26 Harmonic Functions on Groups....Pages 27-32 Some Relations between Volume, Injectivity Radius, and Convexity Radius in Riemannian Manifolds....Pages 33-42 Heat Equation, Proportionality Principle, and Volume of Fundamental Domains....Pages 43-54 Some Remarks on the Fundamental Kernels of a Pseudo-Riemannian Manifold....Pages 55-62 Geodesic Balls in Riemannian Product Manifolds....Pages 63-66 Twisted Exotism....Pages 67-73 On Lie Transformation Groups and the Covariance of Differential Operators....Pages 75-89 Geometrical Interpretations of Scalar Curvature and Regularity of Conformal Homeomorphisms....Pages 91-105 Pfaffian Systems and Transverse Differential Geometry....Pages 107-126 The Curvature Class of an Almost-Complex Manifold....Pages 127-134 Pseudogroups and Linear Connections on a Banach Fibre Bundle....Pages 135-145 Mobility in Categories and Metric Spaces....Pages 147-158 The Tension Field of Maps of Riemannian Manifolds....Pages 159-167 Front Matter....Pages 169-169 Conformal Invariance in Physics....Pages 171-195 Quantum Mechanics of Predictive Poincaré Invariant Systems....Pages 197-214 Scalar Time Functions: Differentiability....Pages 215-224 The Problem of Constraints in General Relativity: Solution of the Lichnerowicz Equation....Pages 225-235 Front Matter....Pages 169-169 Hamiltonian Construction of Predictive Systems....Pages 237-248 Symplectic Manifolds, Dynamical Groups, and Hamiltonian Mechanics....Pages 249-269 Any Space-Time has a Plane Wave as a Limit....Pages 271-275 Curvature Invariants, Characteristic Classes, and the Petrov Classification of Space-Times....Pages 277-289 Back Matter....Pages 291-304