A Hermitian metric on a complex manifold of complex dimension n is called astheno-Kähler if its fundamental 2-form F satisfies the condition ∂∂F n−2 = 0 and it is strong KT if F is ∂∂-closed. We prove that a conformally balanced astheno-Kähler metric on a compact manifod of complex dimension n ≥ 3, whose Bismut connection has (restricted) holonomy contained in SU(n), is necessarily Kähler. We p...

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional nilmanifolds carrying an invariant half-flat structure. MSC classification: Primary 53C25; Secondary 53C29, 17B30 An SU(3)-structure on a manifold of real dimension 6 ...

There has always been a lack of examples of compact manifolds which are minimal sets under the action of the real line, minimal meaning that each orbit is dense in the manifold. All tori admit such an action and G. A. Hedlund [4] has given examples of 3-manifolds having such an action. The action of a group T on a metric space X is said to be distal if for any two distinct points x, y&X the dis...

A left invariant metric on a nilpotent Lie group is called minimal, if it minimizes the norm of the Ricci tensor among all left invariant metrics with the same scalar curvature. Such metrics are unique up to isometry and scaling and the groups admitting a minimal metric are precisely the nilradicals of (standard) Einstein solvmanifolds. If N is endowed with an invariant symplectic, complex or h...

The nilmanifolds admitting Anosov automorphisms correspond to Anosov Lie algebras, which in turn determine very special algebraic units in number fields. By studying properties of these algebraic units using basic field theory, we can rule out many possibilities for a Lie algebra to be Anosov. This technique is useful for the classification of Anosov Lie algebras and hence the classification of...