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- catalog abstract "There has been fundamental progress in complex differential geometry in the last two decades. For one, the uniformization theory of canonical Kähler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. The aim of this monograph is to give an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents the reader with some advanced topics in complex differential geometry not easily found elsewhere. The topics include Calabi-Futaki invariants, extremal Kähler metrics, the Calabi-Yau theorem on existence of Kähler Ricci-flat metrics, and recent progress on Kähler-Einstein metrics with positive scalar curvature. Applications of Kähler-Einstein metrics to the uniformization theory are also discussed. Readers with a good general knowledge of differential geometry and partial differential equations should be able to grasp and appreciate the materials in this monograph.".
- catalog contributor b11907374.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog description "1. Introduction to Kahler manifolds -- 2. Extremal Kahler metrics -- 3. Calabi-Futaki invariants -- 4. Scalar curvature as a moment map -- 5. Kahler-Einstein metrics with non-positive scalar curvature -- 6. Kahler-Einstein metrics with positive scalar curvature -- 7. Applications and generalizations.".
- catalog description "Includes bibliographical references (p. [99]-100) and index.".
- catalog description "There has been fundamental progress in complex differential geometry in the last two decades. For one, the uniformization theory of canonical Kähler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. The aim of this monograph is to give an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents the reader with some advanced topics in complex differential geometry not easily found elsewhere. The topics include Calabi-Futaki invariants, extremal Kähler metrics, the Calabi-Yau theorem on existence of Kähler Ricci-flat metrics, and recent progress on Kähler-Einstein metrics with positive scalar curvature. Applications of Kähler-Einstein metrics to the uniformization theory are also discussed. Readers with a good general knowledge of differential geometry and partial differential equations should be able to grasp and appreciate the materials in this monograph.".
- catalog extent "100 p. ;".
- catalog identifier "0817661948 (alk. paper)".
- catalog identifier "3764361948 (alk. paper)".
- catalog isPartOf "Lectures in mathematics ETH Zürich".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Basel ; Boston, MA : Birkhäuser,".
- catalog subject "515/.73 21".
- catalog subject "Geometry, Differential.".
- catalog subject "Global analysis (Mathematics)".
- catalog subject "Global differential geometry.".
- catalog subject "Kählerian manifolds.".
- catalog subject "Mathematical physics.".
- catalog subject "Mathematics.".
- catalog subject "QA649 .T46 2000".
- catalog tableOfContents "1. Introduction to Kahler manifolds -- 2. Extremal Kahler metrics -- 3. Calabi-Futaki invariants -- 4. Scalar curvature as a moment map -- 5. Kahler-Einstein metrics with non-positive scalar curvature -- 6. Kahler-Einstein metrics with positive scalar curvature -- 7. Applications and generalizations.".
- catalog title "Canonical metrics in Kähler geometry / Gang Tian ; notes taken by Meike Akveld.".
- catalog type "text".