An Introduction to Riemannian Geometry
by Sigmundur Gudmundsson
Publisher: Lund University 2010
Number of pages: 106
The main purpose of these lecture notes is to introduce the beautiful theory of Riemannian Geometry, a still very active area of mathematical research. This is a subject with no lack of interesting examples. They are indeed the key to a good understanding of it and will therefore play a major role throughout this work. Of special interest are the classical Lie groups allowing concrete calculations of many of the abstract notions on the menu.
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by Richard L. Bishop - arXiv
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds.
by Ilkka Holopainen, Tuomas Sahlsten
Based on the lecture notes on differential geometry. From the contents: Differentiable manifolds, a brief review; Riemannian metrics; Connections; Geodesics; Curvature; Jacobi fields; Curvature and topology; Comparison geometry; The sphere theorem.
by Adam Marsh - arXiv
A pedagogical but concise overview of Riemannian geometry is provided in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions and relevant theorems.
by M. Berger - Tata Institute of Fundamental Research
The main topic of these notes is geodesics. Our aim is to give a fairly complete treatment of the foundations of Riemannian geometry and to give global results for Riemannian manifolds which are subject to geometric conditions of various types.