On the weighted orthogonal Ricci curvature
Differential Geometry
2021-11-02 v1 Algebraic Geometry
Complex Variables
Abstract
We introduce the weighted orthogonal Ricci curvature -- a two-parameter version of Ni--Zheng's orthogonal Ricci curvature. This curvature serves as a very natural object in the study of the relationship between the Ricci curvature(s) and the holomorphic sectional curvature. In particular, in determining optimal curvature constraints for a compact K\"ahler manifold to be projective. In this direction, we prove a number of vanishing theorems using the weighted orthogonal Ricci curvature(s) in both the K\"ahler and Hermitian category.
Keywords
Cite
@article{arxiv.2111.00346,
title = {On the weighted orthogonal Ricci curvature},
author = {Kyle Broder and Kai Tang},
journal= {arXiv preprint arXiv:2111.00346},
year = {2021}
}
Comments
18 pages