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. It also introduces Riemannian geometry. Written by a noted mathematician, the text presupposes a knowledge of calculus. Nearly 200 problems. 1935 edition. Unabridged republication of the 1966 Dover edition.
Lectures on Classical Differential Geometry: Second Edition by Dirk J. Struik 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, envelopes, more. Many problems and solutions. Bibliography.
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 Geometry by Heinrich W. Guggenheimer This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.
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.
