Hermitian metrics with vanishing second Chern Ricci curvature
Differential Geometry
2026-04-01 v1 Complex Variables
Abstract
We describe a rigidity phenomenon exhibited by the second Chern Ricci curvature of a Hermitian metric on a compact complex manifold. This yields a characterisation of second Chern Ricci-flat Hermitian metrics on several types of manifolds as well as a range of non-existence results for such metrics.
Keywords
Cite
@article{arxiv.2309.10295,
title = {Hermitian metrics with vanishing second Chern Ricci curvature},
author = {Kyle Broder and Artem Pulemotov},
journal= {arXiv preprint arXiv:2309.10295},
year = {2026}
}
Comments
11 pages