Integrating holomorphic sectional curvatures
Differential Geometry
2023-07-06 v1 Algebraic Geometry
Complex Variables
Abstract
We calculate the -norm of the holomorphic sectional curvature of a K\"ahler metric by representation-theoretic means. This yields a new proof that the holomorphic sectional curvature determines the whole curvature tensor. We then investigate what the holomorphic sectional curvature of a Hermitian metric determines and calculate the -norm of the holomorphic bisectional curvature.
Cite
@article{arxiv.2307.01332,
title = {Integrating holomorphic sectional curvatures},
author = {Gunnar Þór Magnússon},
journal= {arXiv preprint arXiv:2307.01332},
year = {2023}
}
Comments
9 pages, comments welcome