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