Riemannian Geometry by Richard L. Bishop

Small book cover: Riemannian Geometry

Riemannian Geometry

Publisher: arXiv
Number of pages: 67

These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds. Affine connections, geodesics, torsion and curvature, the exponential map, and the Riemannian connection follow quickly.

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