We classify nilmanifolds with an invariant symplectic half-flat structure. We solve the half-flat evolution equations in one example, writing down the resulting Ricci-flat metric. We study the geometry of the orbit space of 6-manifolds with an SU(3)-structure preserved by a U(1) action, giving characterizations in the symplectic half-flat and integrable case.

We show that almost nonnegatively curved m -manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups. We also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds.

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...

We prove that N( f )= |L( f )| for any continuous map f of a given infranilmanifold with Abelian holonomy group of odd order. This theorem is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We will also show that although their fundamental groups are solvable, the infranilmanifolds we consider are in general not solvmanifolds, and hence they cannot be treated using the ...

An electrochemical study using transient techniques of a quinone-type natural product, horminone, has been performed in acetonitrile in the presence of two buffer solutions of pH = 17.2 and pH = 15.5. Using linear sweep voltammetry, it was found that at both pH values the reduction mechanism of horminone involves a monoelectronic charge-transfer step, followed by a protonation step and homogene...

A few years ago, the first example of a closed manifold admitting an Anosov diffeomorphism but no expanding map was given. Unfortunately, this is not explicit and high-dimensional, although its exact dimension unknown due to type construction. In paper, we present family concrete 12-dimensional nilmanifolds with map, where nilmanifold defined as quotient 1-connected nilpotent Lie group by cocom...