A Panoramic View of Riemannian Geometry
(Sprache: Englisch)
This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of...
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This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field.
From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS
From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS
Klappentext zu „A Panoramic View of Riemannian Geometry “
This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS
Inhaltsverzeichnis zu „A Panoramic View of Riemannian Geometry “
0. Vector fields, tensors 1. Tensor Riemannian duality, the connection and the curvature 2. The parallel transport 3. Absolute (Ricci) calculus, commutation formulas 4. Hodge and the Laplacian, Bochners technique 5. Generalizing Gauss-Bonnet, characteristic classes and C. GEOMETRIC MEASURE THEORY AND PSEUDO-HOLOMORPHIC B. HIGHER DIMENSIONS A.THE CASE OF SURFACES IN R3 C. various other bundles 3. Harmonic maps between Riemannian manifolds 4. Low dimensional Riemannian geometry 5. Some generalizations of Riemannian geometry 6. Gromov mm-spaces 7. Submanifolds B. Spinors A. Exterior differential forms (and some others) C. RICCI FLAT KÄHLER AND HYPERKÄHLER MANIFOLDS 6. Kählerian manifolds (Kähler metrics) Chapter XI : SOME OTHER IMPORTANT TOPICS 1. Non compact manifolds 2. Bundles over Riemannian manifolds B. QUATERNIONIC-KÄHLER MANIFOLDS A. G2 AND Spin(7) HIERRACHY : HOLONOMY GROUPS AND KÄHLER MANIFOLDS 1. Definitions and philosophy 2. Examples 3. General structure theorems 4. The classification result 5. The rare cases b. on a given compact manifolds : closures Chapter X : GLOBAL PARALLEL TRANSPORT AND ANOTHER RIEMANNIAN a. collapsing C. THE CASE OF RICCI CURVATURE 12. Compactness, convergence results 13. The set of all Riemannian structures : collapsing B. MORE FINITENESS THEOREMS A. CHEEGERs FINITENESS THEOREM 11. Finiteness results of all Riemannian structures third part : Finiteness, compactness, collapsing and the space D. NEGATIVE VERSUS NONPOSITIVE CURVATURE 10. The negative side : Ricci curvature C. VOLUMES, FUNDAMENTAL GROUP B. QUASI-ISOMETRIES A. INTRODUCTION E. POSSIBLE APPROACHES, LOOKING FOR THE FUTURE 7. Ricci curvature : positive, nonnegative and just below 8. The positive side : scalar curvature 9. The negative side : sectional curvature D. POSITIVITY OF THE CURVATURE OPERATOR C. THE NON-COMPACT CASE B. HOMOLOGY TYPE AND THE FUNDAMENTAL GROUP A. THE KNOWN EXAMPLES 6. The positive side : sectional curvature second part : Curvature of a given sign 1. Int
Bibliographische Angaben
- Autor: M. Berger
- 1st ed. 2003. Corr. 2nd printing 2007, 824 Seiten, 400 Abbildungen, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540653171
- ISBN-13: 9783540653172
- Erscheinungsdatum: 29.06.2007
Sprache:
Englisch
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