Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)

By Thomas A. Ivey

This ebook is an creation to Cartan's method of differential geometry. relevant equipment in Cartan's geometry are the speculation of external differential platforms and the strategy of relocating frames. This ebook offers thorough and sleek remedies of either matters, together with their purposes to either vintage and modern difficulties. It starts off with the classical geometry of surfaces and simple Riemannian geometry within the language of relocating frames, besides an hassle-free advent to external differential platforms. Key recommendations are constructed incrementally with motivating examples resulting in definitions, theorems, and proofs. as soon as the fundamentals of the tools are proven, the authors strengthen purposes and complicated topics.One amazing software is to advanced algebraic geometry, the place they extend and replace vital effects from projective differential geometry. The booklet beneficial properties an advent to $G$-structures and a remedy of the idea of connections. The Cartan equipment can be utilized to procure particular strategies of PDEs through Darboux's technique, the strategy of features, and Cartan's approach to equivalence. this article is appropriate for a one-year graduate direction in differential geometry, and components of it may be used for a one-semester direction. It has a number of routines and examples all through. it is going to even be priceless to specialists in components similar to PDEs and algebraic geometry who are looking to learn the way relocating frames and external differential platforms follow to their fields.

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