Displaying similar documents to “Stability of the tangent bundle and existence of a Kähler-Einstein metric.”

Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections

Julien Keller, Christina Tønnesen-Friedman (2012)

Open Mathematics

Similarity:

We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.

Kähler-Einstein metrics: Old and New

Daniele Angella, Cristiano Spotti (2017)

Complex Manifolds

Similarity:

We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.

On para-Kähler-Norden structures on the tangent bundles

Arif Salimov, Aydin Gezer, Murat Iscan (2012)

Annales Polonici Mathematici

Similarity:

The main purpose of this article is to investigate the paraholomorphy property of the Sasaki and Cheeger-Gromoll metrics by using compatible paracomplex stuctures on the tangent bundle.

Convexity on the space of Kähler metrics

Bo Berndtsson (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

These are the lecture notes of a minicourse given at a winter school in Marseille 2011. The aim of the course was to give an introduction to recent work on the geometry of the space of Kähler metrics associated to an ample line bundle. The emphasis of the course was the role of convexity, both as a motivating example and as a tool.