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Canonical Metrics in Kähler Geometry

Gang Tian (Autor)

Buch | Softcover

VII, 101 Seiten

2000 | 2000
Springer Basel (Verlag)
978-3-7643-6194-5 (ISBN)

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lt;p>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.

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.

"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."

--Publicationes Mathematicae

"This monograph includes an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds."

--Zentralblatt Math

Erscheint lt. Verlag	1.8.2000
Reihe/Serie	Lectures in Mathematics. ETH Zürich
Mitarbeit	Anmerkungen: M. Akveld
Zusatzinfo	VII, 101 p.
Verlagsort	Basel
Sprache	englisch
Maße	178 x 254 mm
Gewicht	460 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Curvature • Differential Geometry • Geometry • Kähler Geometry • manifold • partial differential equation • Partial differential equations
ISBN-10	3-7643-6194-8 / 3764361948
ISBN-13	978-3-7643-6194-5 / 9783764361945
Zustand	Neuware