by Edward Nelson
Publisher: Princeton Univ Pr 1974
Number of pages: 138
These are the lecture notes for the first part of a one-term course on differential geometry given at Princeton in the spring of 1967. They are an expository account of the formal algebraic aspects of tensor analysis using both modern and classical notations.
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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 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.
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 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. This texts has an early introduction to differential forms and their applications to Physics.