Differential Geometry: Lecture Notes
by Dmitri Zaitsev
Publisher: Trinity College Dublin 2004
Number of pages: 49
From the table of contents: Chapter 1. Introduction to Smooth Manifolds; Chapter 2. Basic results from Differential Topology; Chapter 3. Tangent spaces and tensor calculus; Tensors and differential forms; Chapter 4. Riemannian geometry.
Download or read it online for free here:
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 Gabriel Lugo - University of North Carolina at Wilmington
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.
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.