A canonical construction yielding a global view of twistor theory.
A Kummer-type construction of self-dual 4-manifolds.
Algebraic Dimension of Twistor Spaces.
Algebraic dimension of twistor spaces and scalar curvature of anti-self-dual metrics.
Compactifications kähleriennes de voisinages ouverts de cycles géométriquement positifs
Complex Paraconformal Manifolds - their Differential Geometry.
Equivariant connected sums of compact self-dual manifolds.
Fourier-Mukai transform and index theory.
Geometry of some twistor spaces of algebraic dimension one
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
Hyperkähler manifolds
Injectivity of the double fibration transform for cycle spaces of flag domains.
Integral transforms for divisors in and solutions of systems of PDE’s
Komplexní vesmír Rogera Penrose
Properties of operators occurring in the Penrose transform
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.
Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics
We study the Jones and Tod correspondence between selfdual conformal -manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl -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.
Structure fractals and para-quaternionic geometry
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