ar X iv : d g - ga / 9 41 00 05 v 2 1 7 O ct 1 99 4 Hermitian structures and harmonic morphisms in higher dimensional Euclidean spaces

ar X iv : d g - ga / 9 51 20 10 v 2 2 4 M ay 1 99 6 Weierstrass representations for harmonic morphisms on Euclidean spaces and spheres

We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by finding heierarchies of Weierstrass-type representations. This enables us to find new examples of complex-valued harmonic mor-phisms from Euclidean spaces and spheres.

ar X iv : d g - ga / 9 51 10 01 v 1 3 N ov 1 99 5 QUADRATIC HARMONIC MORPHISMS AND O - SYSTEMS

We introduce O-systems (Definition 3.1) of orthogonal transformations of R m , and establish 1 − 1 correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and orthogonal multiplications of the form µ : R n × R m −→ R m , which allow us to solve the existence problems both for O-systems and for umbilical quadratic harmonic morphisms (Theo...

ar X iv : d g - ga / 9 51 00 06 v 1 2 3 O ct 1 99 5 GROUP SYSTEMS , GROUPOIDS , AND MODULI SPACES OF PARABOLIC BUNDLES

ar X iv : a lg - g eo m / 9 41 00 29 v 1 2 7 O ct 1 99 4 Contractions on a manifold polarized by an ample vector bundle

ar X iv : d g - ga / 9 71 00 01 v 1 2 O ct 1 99 7 INTEGRAL INVARIANTS OF 3 - MANIFOLDS

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer [2] and those of Kontsevich [9].