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 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 Gilbert Weinstein - UAB
These notes are for a beginning graduate level course in differential geometry. It is assumed that this is the students' first course in the subject. Thus the choice of subjects and presentation has been made to facilitate a concrete picture.
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 Noel J. Hicks - Van Nostrand
A 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.