The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a potential that generalises Plebanski’s second heavenly equation for hyper-Kahler 4-manifolds. A class of examples of hyper-Hermitian metrics which depend on two arbitrary functions of two complex variables is given. The twistor theory of four-dimensional hyper-Hermitian manifolds is formulated as a com...

This paper classifies Hermitian structures on 6-dimensional nilmanifolds M = Γ\G for which the fundamental 2-form is ∂∂-closed, a condition that is shown to depend only on the underlying complex structure J of M . The space of such J is described when G is the complex Heisenberg group, and explicit solutions are obtained from a limaçon-shaped curve in the complex plane. Related theory is used t...

Complex numbers enter fundamental physics in at least two rather distinct ways. They are needed in quantum theories to make linear diier-ential operators into Hermitian observables. Complex structures appear also, through Hodge duality, in vector and spinor spaces associated with space-time. This paper reviews some of these notions. Charge conjugation in multidimensional geometries and the appe...

Three types of Riemannian submersions whose total space is an almost Hermitian almost contact metric manifold are studied. The study is focused on fundamental properties and the transference of structures. 1. Introduction. In this paper, we discuss some geometric properties of Riemannian submersions whose total space is an almost Hermitian almost contact metric manifold. If the base space is an...

Complex numbers enter fundamental physics in at least two rather distinct ways. They are needed in quantum theories to make linear differential operators into Hermitian observables. Complex structures appear also, through Hodge duality, in vector and spinor spaces associated with space-time. This paper reviews some of these notions. Charge conjugation in multidimensional geometries and the appe...