EUDML

A primary Hopf surface is a compact complex surface with universal cover $ℂ^{2} - {(0, 0)}$ and cyclic fundamental group generated by the transformation $(u, v) \mapsto (α u + λ v^{m}, β v)$ , $m \in ℤ$ , and $α, β, λ \in ℂ$ such that $∣ α ∣ \geq ∣ β ∣ > 1$ and $(α - β^{m}) λ = 0$ . Being diffeomorphic with $S^{3} \times S^{1}$ Hopf surfaces cannot admit any Kähler metric. However, it was known that for $λ = 0$ and $∣ α ∣ = ∣ β ∣$ they admit a locally conformally Kähler metric with parallel Lee form. We here provide the construction of a locally conformally Kähler metric with parallel Lee form for primary Hopf surfaces of class $1$ ( $λ = 0$ ). We also show...

Selfdual Einstein hermitian four-manifolds

Vestislav Apostolov; Paul Gauduchon — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We provide a local classification of selfdual Einstein riemannian four-manifolds admitting a positively oriented hermitian structure and characterize those which carry a hyperhermitian, non-hyperkähler structure compatible with the negative orientation. We show that selfdual Einstein 4-manifolds obtained as quaternionic quotients of $ℍ P^{2}$ and $ℍ H^{2}$ are hermitian.

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La l-forme de torsion d'une variété hermitienne compacte.

Variétés riemanniennes autoduales

Twisteurs et applications harmoniques en dimension 4

Structures de Weyl-Einstein, espace de twisteurs et variétés de type S1 x S3.

Fibrés hermitiens à endomorphisme de Ricci non négatif

Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale

Géométrie hyperkählérienne des espaces hermitiens symétriques complexifiés

Any Hermitian Metric of Constant Non-Positive (Hermitian) Holomorphic Sectional Curvature on a Compact Complex Surface is Kähler.

Locally conformally Kähler metrics on Hopf surfaces

Selfdual Einstein hermitian four-manifolds