Differential Geometry: A First Course in Curves and Surfaces
by Theodore Shifrin
Publisher: University of Georgia 2015
Number of pages: 127
Contents: Curves (Examples, Arclength Parametrization, Local Theory: Frenet Frame, Some Global Results), Surfaces: Local Theory (Parametrized Surfaces and the First Fundamental Form, The Gauss Map and the Second Fundamental Form, The Codazzi and Gauss Equations, Covariant Differentiation, Parallel Translation, and Geodesics) Surfaces: Further Topics (Holonomy and the Gauss-Bonnet Theorem, Hyperbolic Geometry, Surface Theory with Differential Forms, Calculus of Variations and Surfaces of Constant Mean Curvature).
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by Gilbert Weinstein - UAB
These notes are for a beginning graduate level course in differential geometry. It is assumed that this is the students' first course in the subject. Thus the choice of subjects and presentation has been made to facilitate a concrete picture.
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 Wulf Rossmann - University of Ottawa
This is a collection of lecture notes which the author put together while teaching courses on manifolds, tensor analysis, and differential geometry. He offers them to you in the hope that they may help you, and to complement the lectures.
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.