We study invariant Abelian hypercomplex structures on 8-dimensional nilpotent Lie groups. We prove that a group N admitting such a structure is either Abelian or an Abelian extension of a group of type H. We determine the ...

Let (N, J) be a simply connected 2n-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on N compatible with J to be minimal, if it minimizes the norm ...

The aim of this paper is to study self-similar solutions to the symplectic curvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention on the family of symplectic two- and three-step nilpotent ...

In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an application we develop the ...

This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the ...

Let f1, …, fk: M → N be maps between closed manifolds, N(f1, …, fk ) and R(f1, …, fk ) be the Nielsen and the Reideimeister coincidence numbers, respectively. In this note, we relate R(f1, …, fk ) with R(f1, f2 ), …, R(f1, ...

In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction ...

In this work, we consider a family of Gelfand pairs (KnN, N) (inshort (K, N) ) where Nis a two step nilpotent Lie group, and Kis the group oforthogonal automorphisms ofN. This family has a nice analytic property: almos ...

We study generalized complex structures and T-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called ...

We study the geodesic orbit property for nilpotent Lie groups N when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When N acts on ...