Riemannian Manifolds as Metric Spaces and the Geometric Meaning of Sectional and Ricci Curvature

Marcel Berger ()
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Marcel Berger: Institut des Hautes Études Scientifiques IHES

Chapter 6 in A Panoramic View of Riemannian Geometry, 2003, pp 221-297 from Springer

Abstract: Abstract We want to study the metric of a Riemannian manifold. The first tasks to address are: 1. to compute the metric d as defined by equation 4.13 on page 174 (namely itd (p, q) is the infimum of the lengths of curves connecting p to q) 2. to determine if there are curves realizing this distance (called segments or shortest paths or minimal geodesics according to your taste) and 3. to study them.

Keywords: Riemannian Manifold; Symmetric Space; Space Form; Ricci Curvature; Variation Formula (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-3-642-18245-7_6

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