Lectures on Geodesics in Riemannian Geometry
by M. Berger
Publisher: Tata Institute of Fundamental Research 1965
Number of pages: 317
The main topic of these notes is geodesics. Our aim is 1) to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it and 2) to give global results for Riemannian manifolds which are subject to geometric conditions of various types; these conditions involve essentially geodesics.
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In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. The book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading.
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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.
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Course notes for an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.
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The main purpose of these lecture notes is to introduce the beautiful theory of Riemannian Geometry. Of special interest are the classical Lie groups allowing concrete calculations of many of the abstract notions on the menu.