Displaying similar documents to “Some Kähler structures on the tangent bundle of a space form.”

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.

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.

Kähler manifolds of quasi-constant holomorphic sectional curvatures

Georgi Ganchev, Vesselka Mihova (2008)

Open Mathematics

Similarity:

The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants...

QCH Kähler manifolds with κ = 0

Włodzimierz Jelonek (2014)

Colloquium Mathematicae

Similarity:

The aim of this paper is to describe all Kähler manifolds with quasi-constant holomorphic sectional curvature with κ = 0.

4-dimensional anti-Kähler manifolds and Weyl curvature

Jaeman Kim (2006)

Czechoslovak Mathematical Journal

Similarity:

On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.

Stability under deformations of Hermite-Einstein almost Kähler metrics

Mehdi Lejmi (2014)

Annales de l’institut Fourier

Similarity:

On a 4 -dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of compatible almost-complex structures, diffeomorphic at each time to the initial one, and inducing constant Hermitian scalar curvature metrics.

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.