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Riemannian geometry during the second half of the twentieth century / Marcel Berger.

Berger, Marcel, 1927- (författare)
ISBN 0821820524 (alk paper)
Providence, R.I. : American Mathematical Society, cop. 2000.
Engelska ix, 182 p.
Serie: University lecture series ; 17.
  • Bok
Innehållsförteckning Sammanfattning Ämnesord
Stäng  
  • Riemannian Geometry up to 1950. Gauss, Riemann, Christoffel and Levi-Civita. Van Mangoldt, Hadamard, Elie Cartan and Heinz Hopf. Synge, Myers, Preissmann: The use of geometric tools. Hodge, harmonic forms and the Bochner technique: The use of analysis. Allendoerfer, Weil and Chern. Existing tools and a brief look at the new ones. Existing examples and a brief look at the new ones -- Curvature and Topology. Pinching Problems. Curvature of a given sign. Finiteness, compactness, collapsing and the space of all Riemannian structures -- The Geometrical Hierarchy of Riemannian Manifolds: Space Forms. The constant curvature case. Space forms of rank one. Space forms of symmetric spaces of rank larger than one.
  • "In this book, Berger provides a survey of the main developments in Riemannian geometry in the last fifty years, focusing his main attention on the following five areas: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other topics are treated in less detail in a separate section."--BOOK JACKET. 

Ämnesord

Geometry, Riemannian.  (LCSH)

Klassifikation

QA649 (LCC)
516.3/73 (DDC)
53-02 (msc)
01A60 (msc)
Tel (kssb/8 (machine generated))
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