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What is the Best Riemannian Metric on a Compact Manifold?

In: A Panoramic View of Riemannian Geometry

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Listed:
  • Marcel Berger

    (Institut des Hautes Études Scientifiques IHES)

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.

Suggested Citation

  • Marcel Berger, 2003. "What is the Best Riemannian Metric on a Compact Manifold?," Springer Books, in: A Panoramic View of Riemannian Geometry, chapter 11, pages 499-541, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18245-7_11
    DOI: 10.1007/978-3-642-18245-7_11
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