$p$-K\"ahler structures on fibrations and reductive Lie groups

Anna Fino; Gueo Grantcharov; Asia Mainenti

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arXiv · 2601.21849

$p$-K\"ahler structures on fibrations and reductive Lie groups

Anna Fino·Gueo Grantcharov·Asia Mainenti

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Abstract

We investigate the existence of $p$-K\"ahler structures on two classes of complex manifolds: on quasi-regular fibrations, with particular emphasis on complex homogeneous spaces, and on reductive Lie groups endowed with invariant complex structures. In the latter setting, we construct non-regular complex structures on the Lie algebras $\mathfrak{sl}(2m-1,\mathbb{R})$ for $m \ge 2$ and show that these structures admit compatible balanced metrics, providing new explicit examples of balanced manifolds.

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BibTeX RIS

Anna Fino, Gueo Grantcharov, Asia Mainenti. 2026-01-29. $p$-K\"ahler structures on fibrations and reductive Lie groups. https://arxiv.org/abs/2601.21849

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