What is the Best Riemannian Metric on a Compact Manifold?

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

Chapter 11 in A Panoramic View of Riemannian Geometry, 2003, pp 499-541 from Springer

Abstract: Abstract What is the best Riemannian structure on a given compact manifold? René Thom asked the author this question in the Strasbourg mathematics department library around 1960. I should say not only that I liked it, but also that I found it very motivating and frequently advertised it. Moreover, the question is the first problem in the problem list Yau [1296]. It is only recently that I discovered that the question of best metric was posed much earlier by Hopf in Hopf 1932 [730], page 220.

Keywords: Modulus Space; Sectional Curvature; Space Form; Compact Manifold; Chern Class (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-3-642-18245-7_11

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