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It is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by...

Hilbert spaces for massless particles with nonvanishing helicities

Andrzej Karpio (1999)

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

Hyperkähler manifolds

Nigel Hitchin (1991/1992)

Séminaire Bourbaki

Injectivity of the double fibration transform for cycle spaces of flag domains.

Huckleberry, Alan T., Wolf, Joseph A. (2004)

Journal of Lie Theory

Integral transforms for divisors in $ℙ_{n} (ℂ)$ and solutions of systems of PDE’s

Jarolím Bureš, Vladimír Souček, Salomon Ofman (2000)

Czechoslovak Mathematical Journal

Komplexní vesmír Rogera Penrose

Simon G. Gindikin (1986)

Pokroky matematiky, fyziky a astronomie

Properties of operators occurring in the Penrose transform

Zbyněk Šír (2001)

Commentationes Mathematicae Universitatis Carolinae

It is shown that operators occurring in the classical Penrose transform are differential. These operators are identified depending on line bundles over the twistor space.

Scalar-flat Kähler metrics with SU (2) symmetry.

Andrew S. Dancer (1996)

Journal für die reine und angewandte Mathematik

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...

Stability, complex-analyticity and constancy of pluriharmonic maps from compact Kaehler manifolds.

Yoshihiro Ohnita, Seiichi Udagawa (1990)

Mathematische Zeitschrift

Structure fractals and para-quaternionic geometry

Julian Ławrynowicz, Massimo Vaccaro (2011)

Annales UMCS, Mathematica

It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...

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

Paul Gauduchon (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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