We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive ...

We study left-invariant locally conformally Kähler structures on Lie groups, or equivalently, on Lie algebras. We give some properties of these structures in general, and then we consider the special cases when its complex ...

Let g be a 2n-dimensional unimodular Lie algebra equipped with a Hermitian structure (J; F) such that the complex structure J is abelian and the fundamental form F is balanced. We prove that the holonomy group of the ...

In recent papers and books, a global quantization has been developed for unimodular groups of type I. It involves operator-valued symbols defined on the product between the group G and its unitary dual G^ , composed of ...

On each solvable Lie group, there is at most one solv- soliton up to isometry and scaling. This allows us to en- dow several Lie groups that do not admit Einstein metrics (e.g., nilpotent or unimodular solvable Lie groups) ...

We characterize unimodular solvable Lie algebras with Vaisman structures in terms of Kahler flat Lie algebras equipped with a suitable derivation. Using this characterization we obtain algebraic restrictions for the existence ...

Let G be a Lie group of even dimension and let (g,J) be a left invariant anti-Kähler structure on G. In this article we study anti-Kähler structures considering the distinguished cases where the complex structure J is ...

A complete classification of left-invariant closed G2-structures on Lie groups which are extremally Ricci pinched (i.e., dτ=16|τ|2φ+16∗(τ∧τ)), up to equivalence and scaling, is obtained. There are five of them, they are ...