2025/06/04 by Marchidanu, Vlad
#32J27 #32M25 #53C55 #58J05 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.03987
Transversally Kähler foliations are a generalisation of Kähler manifolds, appearing naturally in the complex non-Kähler 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 Kähler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem.