Special structures on almost abelian solvmanifolds

Asia Mainenti; Andrei Moroianu

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arXiv · 2606.09583

Special structures on almost abelian solvmanifolds

Asia Mainenti·Andrei Moroianu

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Abstract

We characterize every almost abelian Lie algebra endowed with an integrable complex structure by a triple, called presentation, consisting of a real number, an element in some vector space and an endomorphism of that vector space. We then classify in terms of presentations the almost abelian Lie algebras admitting $p$-K\"ahler or $p$-pluriclosed structures, and in particular those carrying K\"ahler, balanced, pluriclosed and Gauduchon metrics. Furthermore, we characterize the existence of LCK and Bismut-Ricci flat metrics in this setting.

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Asia Mainenti, Andrei Moroianu. 2026-06-08. Special structures on almost abelian solvmanifolds. https://arxiv.org/abs/2606.09583

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