From Curvature to Topology

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

Chapter 12 in A Panoramic View of Riemannian Geometry, 2003, pp 543-635 from Springer

Abstract: Abstract We have frequently encountered relations between curvature and topology. Among others we can mention the Gauss—Bonnet—Blaschke theorem 28, the von Mangoldt—Hadamard—Cartan theorem 72, Myers’ theorem 63, and Synge’s theorem 64. The topic of curvature and topology has been for some time the most popular and highly developed topic in Riemannian geometry.

Keywords: Riemannian Manifold; Sectional Curvature; Betti Number; Ricci Curvature; Injectivity Radius (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-3-642-18245-7_12

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