Harmonic maps are generalisations of the concept of geodesics. They
encompass many fundamental examples in differential geometry and
have recently become of widespread use in many areas of mathematics
and mathematical physics. This is an accessible introduction to
some of the fundamental connections between differential geometry,
Lie groups, and integrable Hamiltonian systems. The specific goal
of the book is to show how the theory of loop groups can be used to
study harmonic maps. By concentrating on the main ideas and
examples, the author leads up to topics of current research. The
book is suitable for students who are beginning to study manifolds
and Lie groups, and should be of interest both to mathematicians
and to theoretical physicists.
General
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