Natural Operations in Differential Geometry

The literature on natural bundles and natural operators in differential geometry was, until now, scattered in the mathematical journal literature. This monograph collects and presents this material in a unified format. 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 reducing 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. 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 comprehensive bibliography of over 300 items.