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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.
List of contents
Thirty Years of Activity in the Renovation of Mathematical Education.- I-Differential Geometry.- The Scalar Curvature.- On Automorphisms of Spaces of Nonpositive Curvature with Finite Volume.- Harmonic Functions on Groups.- Some Relations Between Volume, Injectivity Radius, and Convexity Radius in Riemannian Manifolds.- Heat Equation, Proportionality Principle, and Volume of Fundamental Domains.- Some Remarks on the Fundamental Kernels of a Pseudo-Riemannian Manifold.- Geodesic Balls in Riemannian Product Manifolds.- Twisted Exotism.- On Lie Transformation Groups and the Covariance of Differential Operators.- Geometrical Interpretations of Scalar Curvature and Regularity of Conformal Homeomorphisms.- Pfaffian Systems and Transverse Differential Geometry.- The Curvature Class of an Almost-Complex Manifold.- Pseudogroups and Linear Connections on a Banach Fibre Bundle.- Mobility in Categories and Metric Spaces.- The Tension Field of Maps of Riemannian Manifolds.- II-Mathematical Physics.- Conformal Invariance in Physics.- Quantum Mechanics of Predictive Poincaré Invariant Systems.- Scalar Time Functions: Differentiability.- The Problem of Constraints in General Relativity: Solution of the Lichnerowicz Equation.- Hamiltonian Construction of Predictive Systems.- Symplectic Manifolds, Dynamical Groups, and Hamiltonian Mechanics.- Any Space-Time Has a Plane Wave as a Limit.- Curvature Invariants, Characteristic Classes, and the Petrov Classification of Space-Times.- Collected Works of A. Lichnerowicz.- Index of Names.
