PreprintCC BY 4.0arXiv
K{ä}hler Einstein manifolds and the Calabi curvature operator
Abstract
In this paper, we study the Calabi curvature operator on K{ä}hler manifolds. First, we prove that if the Calabi curvature operator on K{ä}hler manifolds satisfies (n(n + 1))/2-positive (nonnegative), (n + 1)/2-positive (nonnegative), and ( n−1 )-positive (nonnegative), then the scalar curvature, Ricci curvature, and orthogonal Ricci curvature are positive (nonnegative), respectively. Second, we show that any compact K{ä}hler Einstein manifold satisfying the condition λ1+…+λα≥ −αθ(n,α)λ̅, α≤ n/2 must have nonnegative constant holomorphic sectional curvature.
Related
- Rigidity of Einstein Manifolds under Two Eigenvalue Conditions on the Curvature Operator of the Second Kind
- Holomorphic sectional curvature and the Calabi operator on Kähler C-spaces
- Einstein four-manifolds of positive sectional curvature and ADM mass
- Stability of Einstein 4-manifolds satisfying a chiral curvature condition
- Convergence of cohomogeneity-one Lagrangian mean curvature flow in positive Kähler-Einstein manifolds
BibTeX
@misc{dai2026kähler,
title = {{Kähler Einstein manifolds and the Calabi curvature operator}},
author = {Zhi-Lin Dai and Hai-Ping Fu and Yao Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05106},
eprint = {2609.05106},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05106},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - K{ä}hler Einstein manifolds and the Calabi curvature operator
AU - Zhi-Lin Dai
AU - Hai-Ping Fu
AU - Yao Lu
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05106
UR - https://arxiv.org/abs/2609.05106
AB - In this paper, we study the Calabi curvature operator on K{ä}hler manifolds. First, we prove that if the Calabi curvature operator on K{ä}hler manifolds satisfies (n(n + 1))/2-positive (nonnegative), (n + 1)/2-positive (nonnegative), and ( n−1 )-positive (nonnegative), then the scalar curvature, Ricci curvature, and orthogonal Ricci curvature are positive (nonnegative), respectively. Second, we show that any compact K{ä}hler Einstein manifold satisfying the condition λ_1+…+λ_α≥ −αθ(n,α)λ̅, α≤ n/2 must have nonnegative constant holomorphic sectional curvature.
ER -