Cartan For Beginners Differential Geometry Via Moving Frames And Exterior Differential Systems Graduate Studies In Mathematics ❲SECURE × 2026❳

Cartan for Beginners by Ivey and Landsberg serves as a rigorous, computation-driven bridge between classical differential geometry and the sophisticated geometric PDE theory of Élie Cartan. Departing from the standard coordinate-and-tensor approach, the text systematically develops the method of moving frames (repère mobile) and the theory of exterior differential systems (EDS) as unified tools for solving geometric equivalence problems, characterizing submanifolds, and analyzing overdetermined PDE systems. The intended audience is advanced graduate students and researchers seeking not merely abstract theory but operational mastery in applying Cartan’s methods to concrete geometric problems.

Ivey, Thomas A., and Landsberg, J. M. Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems . Graduate Studies in Mathematics, Vol. 61. Providence, RI: American Mathematical Society, 2003. Cartan for Beginners by Ivey and Landsberg serves

Methodological Synthesis and Pedagogical Review of Cartan For Beginners Ivey, Thomas A