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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
"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
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.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9783764361945
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Condizione: New. There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kaehler metrics has been established in higher dimensions, and many applications have been found, including the u. Codice articolo 5279306
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