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

By Thomas A. Ivey

This e-book is an creation to Cartan's method of differential geometry. valuable tools in Cartan's geometry are the idea of external differential platforms and the strategy of relocating frames. This publication provides thorough and smooth remedies of either matters, together with their functions to either vintage and modern difficulties. It starts with the classical geometry of surfaces and uncomplicated Riemannian geometry within the language of relocating frames, besides an effortless creation to external differential platforms. Key recommendations are built incrementally with motivating examples resulting in definitions, theorems, and proofs. as soon as the fundamentals of the tools are tested, the authors boost functions and complicated topics.One impressive software is to advanced algebraic geometry, the place they extend and replace vital effects from projective differential geometry. The e-book beneficial properties an creation to $G$-structures and a therapy of the speculation of connections. The Cartan equipment is additionally utilized to acquire specific options of PDEs through Darboux's approach, the tactic of features, and Cartan's approach to equivalence. this article is appropriate for a one-year graduate path in differential geometry, and elements of it may be used for a one-semester direction. It has various routines and examples all through. it's going to even be valuable to specialists in parts reminiscent of 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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