A Course Of Differential Geometry
by John Edward Campbell
Publisher: Clarendon Press 1926
Number of pages: 288
Table of 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; The minimal surface; Orthogonal surfaces; etc.
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by Peter W. Michor - American Mathematical Society
Fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.
by Ruslan Sharipov - Samizdat Press
Textbook for the first course of differential geometry. It covers the theory of curves in three-dimensional Euclidean space, the vectorial analysis both in Cartesian and curvilinear coordinates, and the theory of surfaces in the space E.
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.
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.