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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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.
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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.
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Textbook for the first course of differential geometry. It covers the theory of curves in three-dimensional Euclidean space, the vectorial analysis both in Cartesian and curvilinear coordinates, and the theory of surfaces in the space E.
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