Aeppli-Bott-Chern Massey products on non-K\"ahler solvmanifolds

TL;DR

This paper explicitly computes non-trivial Aeppli-Bott-Chern Massey products on certain non-K"ahler solvmanifolds, demonstrating their non-vanishing and absence of astheno-K"ahler metrics.

Contribution

It provides explicit calculations of Aeppli-Bott-Chern Massey products on specific non-K"ahler solvmanifolds, expanding understanding of their complex geometric properties.

Findings

Non-vanishing triple Aeppli-Bott-Chern Massey products on studied manifolds

These manifolds do not admit astheno-K"ahler metrics

Explicit examples include Bigalke-Rollenske and generalized Nakamura manifolds

Abstract

In this paper, we present explicit computations of non-trivial triple $ABC$-Massey products on non-K\"ahler solvmanifolds endowed with an invariant complex structure. We prove that the {\em Bigalke-Rollenske manifold}, the {\em generalized Nakamura manifolds} satisfying some suitable assumptions and compact quotients of the solvable Lie group $\mathbb{C}^{2n}\ltimes_{\rho} \mathbb{C}^{2m}$ have non-vanishing triple $ABC$-Massey products. Furthermore, such manifolds have no astheno-K\"ahler metric.