by Balazs Csikos
Publisher: Eötvös Loránd University 2010
Number of pages: 123
Contents: Basic Structures on Rn, Length of Curves; Curvatures of a Curve; Plane Curves; 3D Curves; Hypersurfaces; Surfaces in the 3-dimensional space; The fundamental equations of hypersurface theory; Topological and Differentiable Manifolds; The Tangent Bundle; The Lie Algebra of Vector Fields; Differentiation of Vector Fields; Curvature; Geodesics.
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by Theodore Shifrin - University of Georgia
Contents: Curves (Examples, Arclength Parametrization, Frenet Frame); Surfaces: Local Theory (Parametrized Surfaces, Gauss Map, Covariant Differentiation, Parallel Translation, Geodesics); Surfaces: Further Topics (Holonomy, Hyperbolic Geometry,...).
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.
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.