Notes on Differential Geometry by Noel J.
Description : 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. Download or read it online for free here: Download link 6. Notes on Differential Geometry by Matt Visser - Victoria University of Wellington In this text the author presents an overview of differential geometry.
Topics covered: Topological Manifolds and differentiable structure; Tangent and cotangent spaces; Fibre bundles; Geodesics and connexions; Riemann curvature; etc. Introduction to Differential Geometry and General Relativity 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.
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. Differential Geometry in Physics 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.
Introduction to Differential Geometry: Curves
This texts has an early introduction to differential forms and their applications to Physics.