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- catalog abstract ""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."--Jacket.".
- catalog contributor b11506159.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description ""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."--Jacket.".
- catalog description "Includes bibliographical references and index.".
- catalog description "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.".
- catalog extent "ix, 182 p. ;".
- catalog identifier "0821820524 (alk. paper)".
- catalog isPartOf "University lecture series (Providence, R.I.) ; 17.".
- catalog isPartOf "University lecture series, 1047-3998 ; v. 17".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "Providence, R.I. : American Mathematical Society,".
- catalog subject "516.3/73 21".
- catalog subject "Geometry, Riemannian.".
- catalog subject "QA649 .B4585 1999".
- catalog tableOfContents "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.".
- catalog title "Riemannian geometry during the second half of the twentieth century / Marcel Berger.".
- catalog type "text".