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140122 ||| eng |
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|a 9783642618765
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| 100 |
1 |
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|a Besse, A. L.
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| 245 |
0 |
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|a Manifolds all of whose Geodesics are Closed
|h Elektronische Ressource
|c by A. L. Besse
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| 250 |
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|a 1st ed. 1978
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1978, 1978
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| 300 |
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|a IX, 264 p
|b online resource
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| 505 |
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|a G. The Kähler Case -- H. An Infinitesimal Blaschke Conjecture -- 6. Harmonic Manifolds -- A. Introduction -- B. Various Definitions, Equivalences -- C. Infinitesimally Harmonic Manifolds, Curvature Conditions -- D. Implications of Curvature Conditions -- E. Harmonic Manifolds of Dimension 4 -- F. Globally Harmonic Manifolds: Allamigeon’s Theorem -- G. Strongly Harmonic Manifolds -- 7. On the Topology of SC- and P-Manifolds -- A. Introduction4 -- B. Definitions -- C. Examples and Counter-Examples -- D. Bott-Samelson Theorem (C-Manifolds) -- E. P-Manifolds -- F. Homogeneous SC-Manifolds -- G. Questions -- H. Historical Note -- 8. The Spectrum of P-Manifolds -- A. Summary -- B. Introduction -- C. Wave Front Sets and Sobolev Spaces -- D. Harmonic Analysis on Riemannian Manifolds -- E. Propagation of Singularities -- F. Proof of the Theorem 8. 9 (J. Duistermaat and V. Guillemin) -- G. A. Weinstein’s result -- H. On the First Eigenvalue ?1=?12 --
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| 505 |
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|a Appendix A. Foliations by Geodesic Circles -- I. A. W. Wadsley’s Theorem -- II. Foliations With All Leaves Compact -- Appendix B. Sturm-Liouville Equations all of whose Solutions are Periodic after F. Neuman -- I. Summary -- II. Periodic Geodesics and the Sturm-Liouville Equation -- III. Sturm-Liouville Equations all of whose Solutions are Periodic -- IV. Back to Geometry with Some Examples and Remarks -- Appendix C. Examples of Pointed Blaschke Manifolds -- I. Introduction -- II. A. Weinstein’s Construction -- III. Some Applications -- Appendix D. Blaschke’s Conjecture for Spheres -- I. Results -- II. Some Lemmas -- III. Proof of Theorem D.4 -- Appendix E. An Inequality Arising in Geometry -- Notation Index
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| 505 |
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|a 0. Introduction -- A. Motivation and History -- B. Organization and Contents -- C. What is New in this Book? -- D. What are the Main Problems Today? -- 1. Basic Facts about the Geodesic Flow -- A. Summary -- B. Generalities on Vector Bundles -- C. The Cotangent Bundle -- D. The Double Tangent Bundle -- E. Riemannian Metrics -- F. Calculus of Variations -- G. The Geodesic Flow -- H. Connectors -- I. Covariant Derivatives -- J. Jacobi Fields -- K. Riemannian Geometry of the Tangent Bundle -- L. Formulas for the First and Second Variations of the Length of Curves -- M. Canonical Measures of Riemannian Manifolds -- 2. The Manifold of Geodesics -- A. Summary -- B. The Manifold of Geodesics -- C. The Manifold of Geodesics as a Symplectic Manifold -- D. The Manifold of Geodesics as a Riemannian Manifold -- 3. Compact Symmetric Spaces of Rank one From a Geometric Point of View -- A. Introduction -- B. The Projective Spaces as Base Spaces of the Hopf Fibrations --
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|a C. The Projective Spaces as Symmetric Spaces -- D. The Hereditary Properties of Projective Spaces -- E. The Geodesics of Projective Spaces -- F. The Topology of Projective Spaces -- G. The Cayley Projective Plane -- 4. Some Examples of C- and P-Manifolds: Zoll and Tannery Surfaces -- A. Introduction -- B. Characterization of P-Metrics of Revolution on S2 -- C. Tannery Surfaces and Zoll Surfaces Isometrically Embedded in (IR3, can) -- D. Geodesics on Zoll Surfaces of Revolution -- E. Higher Dimensional Analogues of Zoll metrics on S2 -- F. On Conformal Deformations of P-Manifolds: A. Weinstein’s Result -- G. The Radon Transform on (S2, can) -- H. V. Guillemin’s Proof of Funk’s Claim -- 5. Blaschke Manifolds and Blaschke’s Conjecture -- A. Summary -- B. Metric Properties of a Riemannian Manifold -- C. The Allamigeon-Warner Theorem -- D. Pointed BlaschkeManifolds and Blaschke Manifolds -- E. Some Properties of Blaschke Manifolds -- F. Blaschke’s Conjecture --
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Differential Geometry
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
0 |
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|a Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
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| 028 |
5 |
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|a 10.1007/978-3-642-61876-5
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-642-61876-5?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 516.36
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