On the weighted orthogonal Ricci curvature
Abstract
We introduce the weighted orthogonal Ricci curvature  a twoparameter version of NiZheng'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 Kähler manifold to be projective. In this direction, we prove a number of vanishing theorems using the weighted orthogonal Ricci curvature(s) in both the Kähler and Hermitian category.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 November 2023
 DOI:
 10.1016/j.geomphys.2023.104783
 arXiv:
 arXiv:2111.00346
 Bibcode:
 2023JGP...19304783B
 Keywords:

 53C55;
 32Q25;
 32Q20;
 32Q05;
 Mathematics  Differential Geometry;
 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables
 EPrint:
 18 pages