Differential Geometry: Lecture Notes
by Dmitri Zaitsev
Publisher: Trinity College Dublin 2004
Number of pages: 49
From the table of contents: Chapter 1. Introduction to Smooth Manifolds; Chapter 2. Basic results from Differential Topology; Chapter 3. Tangent spaces and tensor calculus; Tensors and differential forms; Chapter 4. Riemannian geometry.
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by Richard Koch - University of Oregon
These are differential geometry course notes. From the table of contents: Preface; Curves; Surfaces; Extrinsic Theory; The Covariant Derivative; The Theorema Egregium; The Gauss-Bonnet Theorem; Riemann's Counting Argument.
by Peter W. Michor - American Mathematical Society
Fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.
by John Edward Campbell - Clarendon Press
Contents: Tensor theory; The ground form when n=2; Geodesics in two-way space; Two-way space as a locus in Euclidean space; Deformation of a surface and congruences; Curves in Euclidean space and on a surface; The ruled surface; Minimal surface; etc.
by David W. Henderson - Project Euclid
This is the only book that introduces differential geometry through a combination of an intuitive geometric foundation, a rigorous connection with the standard formalisms, computer exercises with Maple, and a problems-based approach.