Differential Geometry and Relativity

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.