In September 1999 a summer school on Differential Geometry took place in Coimbra. This event was designed to strengthen research in this area in Portugal by improving contacts and discussions among Portuguese mathematicians active in Differential Geometry and related fields and experts from abroad, motivating graduate students to choose this field for their future research, and bringing researchers together for further co-operation on topics from Differential Geometry. A certain number of grants was available and so some foreign students were able to attend. Though participation was open to geometers worldwide, the organisers tried successfully to keep the programme quite limited, so that the participants were not overloaded with information and had some time to think about what had been presented in the lectures.

The school comprised three types of events. There were two 12-hour courses, one by Dirk Ferus on submanifolds and the other one by Izu Vaisman on Poisson and symplectic geometry. Participants could only attend one of the courses since they were simultaneous. Also four invited plenary lectures were offered, giving surveys on some interesting topics of current research in Differential Geometry. Finally, short presentations of research achievements in parallel sessions were possible for those participants who wished it.

This volume contains the texts of the plenary lectures and some original research papers submitted by the participants and related to material presented in the parallel sessions. Initially the two main courses were to be published separately. This will happen with the course given by Vaisman, Lectures on Symplectic and Poisson Geometry appearing within the series Textos de Matemática, série B, no 23, Departamento de Matemática da Universidade de Coimbra, but since Ferus provided only an extended summary we decided to include it with the plenary lectures. The research papers submitted to these proceedings were subject to a peer-reviewing procedure and authors were asked that no version of the same paper be submitted elsewhere for publication.

The organisers express their gratitude to

whose support made the event possible.

Their gratitude is also expressed to Dr. Edeltraud Buchsteiner-Kießling who took much care over the uniform typescript of this volume in TeX and facilitated the installation of an electronic version of this publication.

A. M. d'Azevedo Breda
F. J. Craveiro de Carvalho
J. M. Nunes da Costa
Bernd Wegner

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