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Cover: 9780521688970 | Lectures on Kahler Geometry | Andrei Moroianu | Taschenbuch | Englisch
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Lectures on Kahler Geometry
Taschenbuch von Andrei Moroianu
Sprache: Englisch

66,85 €*

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Beschreibung
Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
Über den Autor
Andrei Moroianu is a Researcher at CNRS and a Professor of Mathematics at Ecole Polytechnique.
Zusammenfassung
Kähler geometry is of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise introduction beginning with a review of basic differential geometry, before moving on to complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. Lastly, several aspects of compact Kähler manifolds are studied: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. Exercises complete each section of the book.
Inhaltsverzeichnis
Introduction; Part I. Basics on Differential Geometry: 1. Smooth manifolds; 2. Tensor fields on smooth manifolds; 3. The exterior derivative; 4. Principal and vector bundles; 5. Connections; 6. Riemannian manifolds; Part II. Complex and Hermitian Geometry: 7. Complex structures and holomorphic maps; 8. Holomorphic forms and vector fields; 9. Complex and holomorphic vector bundles; 10. Hermitian bundles; 11. Hermitian and Kähler metrics; 12. The curvature tensor of Kähler manifolds; 13. Examples of Kähler metrics; 14. Natural operators on Riemannian and Kähler manifolds; 15. Hodge and Dolbeault theory; Part III. Topics on Compact Kähler Manifolds: 16. Chern classes; 17. The Ricci form of Kähler manifolds; 18. The Calabi-Yau theorem; 19. Kähler-Einstein metrics; 20. Weitzenböck techniques; 21. The Hirzebruch-Riemann-Roch formula; 22. Further vanishing results; 23. Ricci-flat Kähler metrics; 24. Explicit examples of Calabi-Yau manifolds; Bibliography; Index.
Details
Erscheinungsjahr: 2014
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780521688970
ISBN-10: 0521688973
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Moroianu, Andrei
Hersteller: Cambridge University Press
Maße: 244 x 170 x 11 mm
Von/Mit: Andrei Moroianu
Erscheinungsdatum: 25.03.2014
Gewicht: 0,325 kg
Artikel-ID: 102105704
Über den Autor
Andrei Moroianu is a Researcher at CNRS and a Professor of Mathematics at Ecole Polytechnique.
Zusammenfassung
Kähler geometry is of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise introduction beginning with a review of basic differential geometry, before moving on to complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. Lastly, several aspects of compact Kähler manifolds are studied: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. Exercises complete each section of the book.
Inhaltsverzeichnis
Introduction; Part I. Basics on Differential Geometry: 1. Smooth manifolds; 2. Tensor fields on smooth manifolds; 3. The exterior derivative; 4. Principal and vector bundles; 5. Connections; 6. Riemannian manifolds; Part II. Complex and Hermitian Geometry: 7. Complex structures and holomorphic maps; 8. Holomorphic forms and vector fields; 9. Complex and holomorphic vector bundles; 10. Hermitian bundles; 11. Hermitian and Kähler metrics; 12. The curvature tensor of Kähler manifolds; 13. Examples of Kähler metrics; 14. Natural operators on Riemannian and Kähler manifolds; 15. Hodge and Dolbeault theory; Part III. Topics on Compact Kähler Manifolds: 16. Chern classes; 17. The Ricci form of Kähler manifolds; 18. The Calabi-Yau theorem; 19. Kähler-Einstein metrics; 20. Weitzenböck techniques; 21. The Hirzebruch-Riemann-Roch formula; 22. Further vanishing results; 23. Ricci-flat Kähler metrics; 24. Explicit examples of Calabi-Yau manifolds; Bibliography; Index.
Details
Erscheinungsjahr: 2014
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780521688970
ISBN-10: 0521688973
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Moroianu, Andrei
Hersteller: Cambridge University Press
Maße: 244 x 170 x 11 mm
Von/Mit: Andrei Moroianu
Erscheinungsdatum: 25.03.2014
Gewicht: 0,325 kg
Artikel-ID: 102105704
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