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).
Home page url
Download or read it online for free here:
by Edward Nelson - Princeton Univ Pr
The lecture notes for the first part of a one-term course on differential geometry given at Princeton in the spring of 1967. They are an expository account of the formal algebraic aspects of tensor analysis using both modern and classical notations.
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 Nigel Hitchin
The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.
by Balazs Csikos - Eötvös Loránd University
Contents: Basic Structures on Rn, Length of Curves; Curvatures of a Curve; Plane Curves; 3D Curves; Hypersurfaces; Surfaces in 3-dimensional space; Fundamental equations of hypersurface theory; Topological and Differentiable Manifolds; etc.