The theory of exterior differential systems provides a framework
for systematically addressing the typically non-linear, and
frequently overdetermined, partial differential equations that
arise in differential geometry. Adaptation of the techniques of
microlocalization to differential systems have led to recent
activity on the foundations of the theory; in particular, the
fundamental role of the characteristic variety in geometric
problems is now clearly established. In this book the general
theory is explained in a relatively quick and concrete manner, and
then this general theory is applied to the recent developments in
the classical problem of isometric embeddings of Riemannian
manifolds.
General
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