Author

Mauro de Andrade Pinto

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Preprint Oct 2026

On the generalized cohomologies of almost abelian solvmanifolds

Generalized complex structures give rise to generalized Dolbeault, Bott--Chern and Aeppli cohomologies. We study these cohomologies for invariant generalized complex structures on almost abelian Lie algebras $\mathfrak g_A=\mathbb R e_0\ltimes_A\mathfrak h$, where $\mathfrak h$ is an abelian ideal of codimension one, a...

Mauro de Andrade Pinto, Letícia Camponês Do Brasil Maia, Leonardo F. Cavenaghi et al. · 0 citations

Preprint Aug 2026

On the generalized geometry of almost abelian solvmanifolds

We study left-invariant generalized complex structures on almost abelian Lie groups $G_A$ with Lie algebra $\mathfrak{g}_A=\mathbb{R} e_0\ltimes_A\mathfrak{h}$, where $\mathfrak{h}$ is an abelian ideal of codimension one, and on their compact quotients. First, when $A$ is diagonalizable over $\mathbb{R}$, we characteri...

Mauro de Andrade Pinto, Letícia Camponês Do Brasil Maia, Leonardo F. Cavenaghi et al. · 1 citation · ⚡1

Preprint Aug 2026

On the geometry and cohomology of almost abelian solvmanifolds

We study left-invariant generalized complex structures on almost abelian Lie groups $G_A = \mathbb{R} \ltimes_{e^{tA}} \mathbb{R}^{d}$, and on the associated solvmanifolds. Our starting point is that the $\mathbf{i}$-eigenspace $\mathfrak{L}$ of such a structure is itself an almost abelian complex Lie algebra, a fact t...

Mauro de Andrade Pinto, Letícia Camponês Do Brasil Maia, Leonardo F. Cavenaghi et al. · 0 citations