Course of Differential Geometry
by Ruslan Sharipov
Publisher: Samizdat Press 2004
Number of pages: 132
This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject. The book is devoted to the firs acquaintance with the differential geometry. Therefore it begins with the theory of curves in three-dimensional Euclidean space E. Then the vectorial analysis in E is stated both in Cartesian and curvilinear coordinates, afterward the theory of surfaces in the space E is considered.
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by John Edward Campbell - Clarendon Press
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; Minimal surface; etc.
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 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 Dmitri Zaitsev - Trinity College Dublin
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.