Differential Geometry Of Three Dimensions
by C.E. Weatherburn
Publisher: Cambridge University Press 1955
Number of pages: 281
The more elementary parts of the subject are discussed in Chapters I-XI. The remainder of the book is devoted to differential invariants for a surface and their applications. By the use of vector methods the presentation of the subject is both simplified and condensed, and students are encouraged to reason geometrically rather than analytically.
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by Stefan Waner
Smooth manifolds and scalar fields, tangent vectors, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, the Riemann curvature tensor, premises of general relativity.
by Theodore Shifrin - University of Georgia
Contents: Curves (Examples, Arclength Parametrization, Frenet Frame); Surfaces: Local Theory (Parametrized Surfaces, Gauss Map, Covariant Differentiation, Parallel Translation, Geodesics); Surfaces: Further Topics (Holonomy, Hyperbolic Geometry,...).
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 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.