Notes on Differential Geometry
by Noel J. Hicks
Publisher: Van Nostrand 1965
Number of pages: 183
A great 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. It thus makes a great reference book for anyone working in any of these fields.
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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 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 Richard Koch - University of Oregon
These are differential geometry course notes. From the table of contents: Preface; Curves; Surfaces; Extrinsic Theory; The Covariant Derivative; The Theorema Egregium; The Gauss-Bonnet Theorem; Riemann's Counting Argument.
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.