$p$-K\"ahler structures on nilmanifolds and holomorphically parallelizable manifolds

Ettore Lo Giudice; Asia Mainenti

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arXiv · 2607.29506

$p$-K\"ahler structures on nilmanifolds and holomorphically parallelizable manifolds

Ettore Lo Giudice·Asia Mainenti

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Abstract

We prove the Alessandrini-Bassanelli conjecture on nilmanifolds with nilpotent complex structures and on holomorphically parallelizable solvmanifolds. As a consequence, we classify holomorphically parallelizable solvmanifolds admitting $p$-K\"ahler structures, for lower values of $p$. We further provide new examples of $(n-2)$-K\"ahler manifolds, in the setting of compact holomorphically parallelizable manifolds with reductive universal cover.

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BibTeX RIS

Ettore Lo Giudice, Asia Mainenti. 2026-07-31. $p$-K\"ahler structures on nilmanifolds and holomorphically parallelizable manifolds. https://arxiv.org/abs/2607.29506

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