$p$-symplectic and $p$-pluriclosed structures on solvmanifolds

Ettore Lo Giudice; Adriano Tomassini

$p$-symplectic and $p$-pluriclosed structures on solvmanifolds

Differential Geometry 2024-07-17 v1

Authors: Ettore Lo Giudice , Adriano Tomassini

Abstract

Let $(M,J)$ be a $n$ -dimensional complex manifold: a $p$ -K\"ahler structure (resp. $p$ -symplectic structure) on $M$ is a real, closed $(p,p)$ -transverse form $\Omega$ (resp. real, closed $2p$ -form whose $(p,p)$ -component is transverse). We give obstructions to the existence of such structures on compact complex manifolds. We provide several families of compact complex manifolds which admit both $(n-1)$ -symplectic structures and special Hermitian metrics.

Keywords

symplectic geometry complex manifold solvmanifold Kähler structure Hermitian metric

Cite

@article{arxiv.2407.11526,
  title  = {$p$-symplectic and $p$-pluriclosed structures on solvmanifolds},
  author = {Ettore Lo Giudice and Adriano Tomassini},
  journal= {arXiv preprint arXiv:2407.11526},
  year   = {2024}
}

$p$-symplectic and $p$-pluriclosed structures on solvmanifolds

Abstract

Keywords

Cite

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