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arXiv · 2111.00346

On the weighted orthogonal Ricci curvature

Kyle Broder·Kai Tang
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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.

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Kyle Broder, Kai Tang. 2021-10-30. On the weighted orthogonal Ricci curvature. https://arxiv.org/abs/2111.00346

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