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Natural Operations in Differential Geometry (Hardcover, 1993 ed.)
Loot Price: R3,744
Discovery Miles 37 440
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Natural Operations in Differential Geometry (Hardcover, 1993 ed.)
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The literature on natural bundles and natural operators in
differential geometry, was until now, scattered in the mathematical
journal literature. This book is the first monograph on the
subject, collecting this material in a unified presentation. The
book begins with an introduction to differential geometry stressing
naturality and functionality, and the general theory of connections
on arbitrary fibered manifolds. The functional approach to
classical natural bundles is extended to a large class of
geometrically interesting categories. Several methods of finding
all natural operators are given and these are identified for many
concrete geometric problems. After reduction each problem to a
finite order setting, the remaining discussion is based on
properties of jet spaces, and the basic structures from the theory
of jets are therefore described here too in a self-contained
manner. The relations of these geometric problems to corresponding
questions in mathematical physics are brought out in several places
in the book, and it closes with a very comprehensive bibliography
of over 300 items. This book is a timely addition to literature
filling the gap that existed here and will be a standard reference
on natural operators for the next few years.
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