Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant problems and solutions. Bibliography.
Here's a sample of other books in this Dover category
Differential Geometry by Erwin Kreyszig An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.
Differential Geometric Structures by Walter A. Poor This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Differential Geometry by William C. Graustein This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of 3 dimensions, using vector notation and technique. Nearly 200 problems.1935 edition.
Differential Topology: An Introduction by David B. Gauld This text covers topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, tangent spaces, vector fields and integral curves, Whitney's embedding theorem, more. Includes 88 helpful illustrations. 1982 edition.
Introduction to Differentiable Manifolds by Louis Auslander, Robert E. MacKenzie This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.
Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces by Richard Courant An examination of approaches to easy-to-understand but difficult-to-solve mathematical problems, this classic text explores conformal mapping on parallel-slit domains, Plateau's problem, the general problem of Douglas, more. 1950 edition.
The Elementary Differential Geometry of Plane Curves by R. H. Fowler This precise account of elementary differential properties of plane curves provides a link between analysis and more complicated geometrical theorems, offering background and practice to geometry and analysis students. 1920 edition.
