Year: 2026
Type: preprint
Abstract: We prove that the Fino--Vezzoni conjecture holds on every compact complex manifold carrying a Hermitian connection with parallel torsion. More precisely, if a compact connected complex manifold carries a Hermitian metric $g$ and a Hermitian connection $D$ with $DT^D=0$, then the coexistence of a balanced metric and a pluriclosed metric forces the existence of a $D$-parallel Kähler metric. The proof combines a holonomy symmetrization onto $D$-parallel forms with a finite-dimensional volume-maximization argument. In particular, the conjecture holds on every compact Bismut torsion-parallel manifold. In the non-balanced case, the obstruction of Zhao--Zheng yields the stronger conclusion that balanced and pluriclosed metrics cannot coexist.
Source: arXiv (Cornell University)
Authors: Chen, Shuwen, Zheng, Fangyang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214176764