Geometry of Manifolds

ISBN-13: 9780821829233 / Angielski / Twarda / 2001 / 273 str.

Usa) Urbana Richard (University Of Illinois Bishop; Richard Crittenden

Opis

The authors' purpose in writing this title is to put material which they found stimulating and interesting as graduate students into form. It is intended for individual study and for use as a text for graduate level courses such as the one from which this material stems, given by Professor W. Ambrose at MIT in 1958-1959. Previously the material had been organized in roughly the same form by him and Professor I.M. Singer, and they in turn drew upon the work of Ehresmann, Chern, and E. Cartan. The authors' contributions have been primarily to fill out the material with details, asides and problems, and to alter notation slightly. They believe that this subject matter, besides being an interesting area for specialization, lends itself especially to a synthesis of several branches of mathematics, and thus should be studied by a wide spectrum of graduate students so as to break away from narrow specialization and see how their own fields are related and applied in other fields. Part of this subject should be of interest not only to those working in geometry, but also to those in analysis, topology, algebra, and even probability.