Canonical Metrics in Kähler Geometry
(Sprache: Englisch)
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...
Leider schon ausverkauft
versandkostenfrei
Buch (Kartoniert)
69.54 €
34 DeutschlandCard Punkte
sammeln
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenlose Rücksendung
- Ratenzahlung möglich
Produktdetails
Produktinformationen zu „Canonical Metrics in Kähler Geometry “
Klappentext zu „Canonical Metrics in Kähler Geometry “
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. This monograph gives an introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere.
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.
Inhaltsverzeichnis zu „Canonical Metrics in Kähler Geometry “
1 Introduction to Kähler manifolds.- 1.1 Kähler metrics.- 1.2 Curvature of Kähler metrics.- 2 Extremal Kähler metrics.- 2.1 The space of Kähler metrics.- 2.2 A brief review of Chern classes.- 2.3 Uniformization of Kähler-Einstein manifolds.- 3 Calabi-Futaki invariants.- 3.1 Definition of Calabi-Futaki invariants.- 3.2 Localization formula for Calabi-Futaki invariants.- 4 Scalar curvature as a moment map.- 5 Kähler-Einstein metrics with non-positive scalar curvature.- 5.1 The Calabi-Yau Theorem.- 5.2 Kähler-Einstein metrics for manifolds with c1(M) 0.- 6 Kähler-Einstein metrics with positive scalar curvature.- 6.1 A variational approach.- 6.2 Existence of Kähler-Einstein metrics.- 6.3 Examples.- 7 Applications and generalizations.- 7.1 A manifold without Kähler-Einstein metric.- 7.2 K-energy and metrics of constant scalar curvature.- 7.3 Relation to stability.
Bibliographische Angaben
- Autor: Gang Tian
- 2000, 2000, 101 Seiten, Maße: 17,8 x 25,4 cm, Kartoniert (TB), Englisch
- Mitarbeit:Akveld, M.
- Verlag: Springer
- ISBN-10: 3764361948
- ISBN-13: 9783764361945
- Erscheinungsdatum: 01.08.2000
Sprache:
Englisch
Rezension zu „Canonical Metrics in Kähler Geometry “
"This little monograph offers an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. ...The author presents some advanced topics which are hard [to] find elsewhere... This graduate course on Kähler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry."
Kommentar zu "Canonical Metrics in Kähler Geometry"
0 Gebrauchte Artikel zu „Canonical Metrics in Kähler Geometry“
| Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
|---|
Schreiben Sie einen Kommentar zu "Canonical Metrics in Kähler Geometry".
Kommentar verfassen