Differential Geometry Proceedings of the Nordic Summer School held i
The Nordic Summer School 1985 presented to young researchers the mathematical aspects of the ongoing research stemming from the study of field theories in physics and the differential geometry of fibre bundles in mathematics. The volume includes papers, o
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1263 V. L. Hansen (Ed.)
Differential Geometry Proceedings of the Nordic Summer School held in Lyngby, Denmark Jul. 29 - Aug. 9, 1985
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
1263 V. L. Hansen (Ed.)
Differential Geometry Proceedings of the Nordic Summer School held in Lyngby, Denmark Jul. 29 - Aug. 9, 1985
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editor
Vagn Lundsgaard Hansen Mathematical Institute The Technical University of Denmark Building 303, DK-28000 Lyngby, Denmark
Mathematics Subject Classification (1980): 32C 10; 32H 10; 53C05; 53C20; 53C55; 53C80; 58E05; 58E11; 58E20; 58G30; 81E10
ISBN 3-540-18012-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18012-5 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
Preface During the period 29 July - 9 August 1985 a Nordic Summer School in mathematics was held at the Technical University of Denmark in Lyngby. The subject of the summer school was "Differential Geometry with Applications". The school was attended by 81 participants and had 8 main lecturers. In addition to the main lectures. there was a series of seminars by the participants. The main reason for choosing differential geometry as the subject for the 1985 Nordic Summer School in mathematics was that the last two decades have witnessed a new strong interaction between mathematics and physics originating in the study of differential geometry of fibre bundles in mathematics and field theories in physics. For many physicists the goal is to find a theory combining all known forces of nature. and it appears that the so-called gauge theories. which in the language of differential geometry correspond to connections in fibre bundles. may provide an answer. Any reasonable field theory is based on a variational principle. and the extremals for the associated differential geometric variational problem are the solutions searched for. Normally. this leads to problems concerning nonlinear (partial differential) equations on manifolds. The purpose of the summer school was to present some of the important mathematical tools. methods. and results necessary for doing research within differential geometry and its above mentioned applications in theoretical physics. The overall structure of the final program for the
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