Elementary Differential Geometry

by Barrett O'Neill

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

Genres: Mathematics, Science, Academic, Reference, Geometry

422 pages, Kindle Edition

First published June 1, 1966

Reviews

[Mark Pedigo]

While studying my PhD, a course in differential geometry (with attached qualifier) was required. This book saved my ass. Start here, then delve into the graduate level stuff.

[Chris]

boring and dry

[Hadi]

This was the textbook for Net Math 423 in UIUC, so I spent plenty of time reading it & solving its problems. Prerequisites for the book were Linear Algebra & Multi-variable calculus, but some proof writing experience would have been very helpful.

I took the course after 13 years of break from university, and I was a CS major back then. So, I had to put lots of energy to work through the course. In the end, it worked well.

[Muhammad Shazib]

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