Differential Geometry and Mathematical Physics : Lectures Given at the Meetings of the Belgian Contact Group on Differential Geometry Held at Liège, May 2–3, 1980 and at Leuven, February 6–8, 1981

This volume contains the text of the lectures which were given at the Differential Geometry Meeting held at Liege in 1980 and at the Differential Geometry Meeting held at Leuven in 1981. The first of these meetings was more orientated toward mathematical physics; the second has a stronger flavour of analysis. The Editors are pleased to thank the lectures who contributed scientifically to these two meetings. They are also grateful to Professor M. F1ato who has encouraged publication of these contributions in the Mathematical Physics Studies Series. We also thank the F.N.R.S. who supported financially the Contact group in differential geometry. The Universite de Liege and the Katholieke Universiteit Leuven which have given us a warm hospitality have contributed to the success of these meetings. We express our gratitude. The Editors. M. Caken et al. (6ds.), Differential Geametry and Mathematical Physics, vii. vii Copyright e 1983 by D. Reidel Publishing Company. Lectures given at the Meeting of the Belgian Contact Group on Differential Geometry held at Liege, May 2-3,1980 SIMULTANEOUS DEFORMATIONS OF A LIE ALGEBRA AND ITS MODULES D. Arnal University of Dijon INTRODUCTION We expose here some results which are obtained by a team at the University of Dijon. This team included Jean-Claude Cortet, Georges Pinczon and myself. Front Matter....Pages i-vii Front Matter....Pages 1-1 Simultaneous Deformations of a Lie Algebra and its Modules....Pages 3-15 How to Connect Exponential Integrals to Optimal Process ?....Pages 17-25 Invariance of Maxwell’s Equations....Pages 27-29 On the Classification of Manifolds Foliated by the Action of a Nilpotent Lie Group....Pages 31-35 Heat, Cold and Geometry....Pages 37-68 Deformations of Algebras Associated with a Symplectic Manifold....Pages 69-83 Differential Deformations with Constant Coefficients....Pages 85-94 Front Matter....Pages 95-95 Some Aspects of Theoretical Physics Relating to Harmonic Maps....Pages 97-104 Stability and Self-Duality of Yang-Mills Fields....Pages 105-106 Embedded 2-Spheres in R 3 ....Pages 107-130 Local Chevalley Cohomologies of the Dynamical Lie Algebra of a Symplectic Manifold....Pages 131-136 The Spin Polarizer....Pages 137-147 Variational Theory in Fibre Bundles: Examples....Pages 149-158 Curvatures of Tubes about Submanifolds....Pages 159-166 Almost Symmetric Spaces....Pages 167-172 Minimal Surfaces and Weyl Groups....Pages 173-175 Some Aspects of Harmonic Maps from a Surface to Complex Projective Space....Pages 177-186 Back Matter....Pages 187-188 Lectures given at the meetings of the Belgian Contact Group on Differential Geometry held at Liege, May 2-3, 1980 and at Leuven, February 6-8, 1981