An Aubin-Yau theorem for transversally K\"ahler foliations
Differential Geometry
2025-06-05 v1 Analysis of PDEs
Complex Variables
Abstract
Transversally K\"ahler foliations are a generalisation of K\"ahler manifolds, appearing naturally in the complex non-K\"ahler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem adapt to the transversally K\"ahler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem.
Keywords
Cite
@article{arxiv.2506.03987,
title = {An Aubin-Yau theorem for transversally K\"ahler foliations},
author = {Vlad Marchidanu},
journal= {arXiv preprint arXiv:2506.03987},
year = {2025}
}