# On a generalized Calabi-Yau equation

## TL;DR

This paper extends a non-existence result for the generalized Calabi-Yau equation, originally proved in complex dimension 2, to manifolds of arbitrary dimension, advancing understanding in almost-Kähler geometry.

## Contribution

It generalizes a key non-existence theorem for the generalized Calabi-Yau equation beyond complex dimension 2 to all dimensions.

## Key findings

- Non-existence result extended to arbitrary dimensions.
- Supports the conjecture about solutions in almost-Kähler manifolds.
- Provides new insights into the structure of the generalized Calabi-Yau equation.

## Abstract

Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-K\"ahler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension 2.