In an earlier paper we developed the classification of weakly symmetric pseudo–Riemannian manifolds $G/H$, where $G$ is a semisimple Lie group and $H$ reductive subgroup. We derived from cases compact. As consequence obtained Lorentz signature $(n-1,1)$ trans-Lorentzian $(n-2,2)$. Here work out pseudo-Riemannian nilmanifolds $G/H$ for case $G=N \rtimes H$ with compact $N$ nilpotent. It turns th...

We associate with each graph (S, E) a 2-step simply connected nilpotent Lie group N and a lattice Γ in N . We determine the group of Lie automorphisms of N and apply the result to describe a necessary and sufficient condition, in terms of the graph, for the compact nilmanifold N/Γ to admit an Anosov automorphism. Using the criterion we obtain new examples of compact nilmanifolds admitting Anoso...

Let M = Γ\G be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result in [5] for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structu...

The (multivalued) higher logarithms are interpreted, by studying their monodromy, as giving well-defined maps from P¿ — (3 points} into certain complex nilmanifolds with C*-actions. The purpose of this note is to exhibit a family of unipotent representations of Z * Z arising naturally from the monodromy of the higher logarithms ln¿. (see [4]), and thereby interpret each ln¿. as yielding a well-...

Anosov diffeomorphisms on closed Riemannian manifolds are a type of dynamical systems exhibiting uniform hyperbolic behavior. Therefore, their properties intensively studied, including which spaces allow such diffeomorphism. It is conjectured that any manifold admitting an diffeomorphism homeomorphic to infra-nilmanifold, is, compact quotient 1-connected nilpotent Lie group by discrete isometri...