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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.
List of contents
Liège, May 2 - 3, 1980.- Simultaneous deformations of a Lie algebra and its modules.- How to connect exponential integrals to optimal process?.- Invariance of Maxwell's equations.- On the classification of manifolds foliated by the action of a nilpotent Lie group.- Heat, cold and geometry.- Deformations of algebras associated with a symplectic manifold.- Differential deformations with constant coefficients.- Leuven, February 6 - 8, 1981.- Some aspects of theoretical physics relating to harmonic maps.- Stability and self-duality of Yang-Mills fields.- Embedded 2-spheres in ?3.- Local Chevalley cohomologies of the dynamical Lie algebra of a symplectic manifold.- The spin polarizer.- Variational theory in fibre bundles: examples.- Curvatures of tubes about submanifolds.- Almost symmetric spaces.- Minimal surfaces and Weyl groups.- Some aspects of harmonic maps from a surface to complex projective space.
