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 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.
by Noel J. Hicks - Van Nostrand
A concise introduction to differential geometry. The ten chapters of Hicks' book contain most of the mathematics that has become the standard background for not only differential geometry, but also much of modern theoretical physics and cosmology.
by C.E. Weatherburn - Cambridge University Press
The book is devoted to differential invariants for a surface and their applications. By the use of vector methods the presentation is both simplified and condensed, and students are encouraged to reason geometrically rather than analytically.
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.