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On K\'ahler manifolds with non-negative mixed curvature
- Publication Year :
- 2024
-
Abstract
- In this work, we investigate compact K\"ahler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional curvature, which covers various notions of curvature considered in the literature. Specifically, we prove a splitting theorem, analogous to the Cheeger-Gromoll splitting theorem, for complete K\"ahler manifolds with non-negative mixed curvature containing a line, and then establish a structure theorem for compact K\"ahler manifolds with non-negative mixed curvature. We also show that the Hodge numbers of compact K\"ahler manifolds with quasi-positive mixed curvature must vanish. Both results are based on the conformal perturbation method.<br />Comment: 29 pages
- Subjects :
- Mathematics - Differential Geometry
Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.14043
- Document Type :
- Working Paper