Notes on Differential Geometry
by Matt Visser
Publisher: Victoria University of Wellington 2011
Number of pages: 246
In this text the author presents an overview of differential geometry, also known as the theory of manifolds. Topics covered: Topological Manifolds and differentiable structure; Tangent and cotangent spaces; Fibre bundles; Geodesics and connexions; Riemann curvature; Exterior differential forms; Lie derivatives; etc.
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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.
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 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.