Differential Geometry and Relativity

1. Front Matter

   Pages I-XI

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2. Thirty Years of Activity in the Renovation of Mathematical Education

   1. Thirty Years of Activity in the Renovation of Mathematical Education

      • R. Couty, A. Revuz

      Pages 1-2

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3. Differential Geometry

   1. Front Matter

      Pages 3-3

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   2. The Scalar Curvature

      • T. Aubin

      Pages 5-18

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   3. On Automorphisms of Spaces of Nonpositive Curvature with Finite Volume

      • Geneviève Avérous, Shoshichi Kobayashi

      Pages 19-26

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   4. Harmonic Functions on Groups

      • A. Avez

      Pages 27-32

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   5. Some Relations between Volume, Injectivity Radius, and Convexity Radius in Riemannian Manifolds

      • M. Berger

      Pages 33-42

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   6. Heat Equation, Proportionality Principle, and Volume of Fundamental Domains

      • Robert S. Cahn, Peter B. Gilkey, Joseph A. Wolf

      Pages 43-54

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   7. Some Remarks on the Fundamental Kernels of a Pseudo-Riemannian Manifold

      • E. Combet, C. Moreno

      Pages 55-62

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   8. Geodesic Balls in Riemannian Product Manifolds

      • Alfred Gray

      Pages 63-66

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   9. Twisted Exotism

      • S. Halperin, D. Lehmann

      Pages 67-73

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   10. On Lie Transformation Groups and the Covariance of Differential Operators

       • Yvette Kosmann

       Pages 75-89

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   11. Geometrical Interpretations of Scalar Curvature and Regularity of Conformal Homeomorphisms

       • Jacqueline Lelong-Ferrand

       Pages 91-105

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   12. Pfaffian Systems and Transverse Differential Geometry

       • Paulette Libermann

       Pages 107-126

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   13. The Curvature Class of an Almost-Complex Manifold

       • Pierre Molino

       Pages 127-134

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   14. Pseudogroups and Linear Connections on a Banach Fibre Bundle

       • Pham Mau Quan

       Pages 135-145

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   15. Mobility in Categories and Metric Spaces

       • S. A. Robertson

       Pages 147-158

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   16. The Tension Field of Maps of Riemannian Manifolds

       • T. J. Willmore

       Pages 159-167

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4. Mathematical Physics

   1. Front Matter

      Pages 169-169

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   2. Conformal Invariance in Physics

      • F. Bayen

      Pages 171-195

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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.

• curvature
• differential geometry
• geometry
• manifold
• mathematical physics
• mechanics
• operator
• quantum mechanics
• transformation

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