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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.

Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics

David M J. Calderbank, Henrik Pedersen (2000)

Annales de l'institut Fourier

We study the Jones and Tod correspondence between selfdual conformal $4$ -manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl $3$ -manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalar-flat Kähler metrics and hypercomplex structures with symmetry. We also show that in the presence...

Smooth, but not Complex-Analytic Pluripolar Sets.

J.E. Fornaess, K. Diederich (1982)

Manuscripta mathematica

Some Hermite Metrics in Complex Finsler Spaces

Irena Čomić, Jovanka Nikić (1994)

Publications de l'Institut Mathématique

Some Hermite metrics in complex Finsler spaces.

Čomić, Irena, Nikić, Jovanka (1994)

Publications de l'Institut Mathématique. Nouvelle Série

Special Einstein’s equations on Kähler manifolds

Irena Hinterleitner, Volodymyr Kiosak (2010)

Archivum Mathematicum

This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov’s classification of Riemannian manifolds according to special properties of the energy-momentum tensor to Kähler manifolds. We show that in this case the number of classes reduces.

Spinorial solution associated to a radially symmetric radiation field in general relativity

Colber G. Oliveira, Nazira Arbex (1972)

Annales de l'I.H.P. Physique théorique

Superminimal fibres in an almost Hermitian submersion

Bill Watson (2000)

Bollettino dell'Unione Matematica Italiana

Se la varietà base, $N$ , di una submersione quasi-Hermitiana, $f : M \to N$ , è una $G_{1}$ -varietà e le fibre sono subvarietà superminimali, allora lo spazio totale, $M$ , è $G_{1}$ . Se la varietà base, $N$ , è Hermitiana e le fibre sono subvarietà bidimensionali e superminimali, allora lo spazio totale, $M$ , è Hermitiano.

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