New hyper-Käahler structures on tangent bundles

Xuerong Qi; Linfen Cao; Xingxiao Li

Displaying similar documents to “New hyper-Käahler structures on tangent bundles”

On a generalized Calabi-Yau equation

Hongyu Wang, Peng Zhu (2010)

Annales de l’institut Fourier

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Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension $2$ .

Compatible complex structures on twistor space

Guillaume Deschamps (2011)

Annales de l’institut Fourier

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Let $M$ be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space $Z$ admits a natural metric. The aim of this article is to study properties of complex structures on $Z$ which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on $M$ (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space $Z$ .

Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact $3$ -structure

Francisco Martín Cabrera (1998)

Czechoslovak Mathematical Journal

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We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds...

Yang-Mills bar connections over compact Kähler manifolds

Hông Vân Lê (2010)

Archivum Mathematicum

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In this note we introduce a Yang-Mills bar equation on complex vector bundles $E$ provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on $E$ can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections...

Displaying similar documents to “New hyper-Käahler structures on tangent bundles”

On a generalized Calabi-Yau equation

Compatible complex structures on twistor space

Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact 3 -structure

Yang-Mills bar connections over compact Kähler manifolds

Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact $3$ -structure