Kähler 爱因斯坦流形与卡拉比曲率算子

中文摘要 AI 辅助

本文研究卡拉比流形上的卡拉比曲率算子。首先，证明若卡拉比流形上的卡拉比曲率算子满足$\frac{n\left(n + 1\right)}{2}$正（非负）、$\frac{n + 1}{2}$正（非负）、$\left( n-1 \right)$正（非负），则对应标量曲率、里奇曲率、正交里奇曲率分别为正（非负）。其次，证明满足条件$$\lambda_1+\dots+\lambda_{\alpha}\ge -{\alpha}\theta(n,{\alpha})\bar\lambda,\; {\alpha}\le \frac{n}{2}$$的任意紧卡拉比爱因斯坦流形必具有非负常全纯截面曲率。

英文摘要

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 $\frac{n\left(n + 1\right)}{2}$-positive (nonnegative), $\frac{n + 1}{2}$-positive (nonnegative), and $\left( n-1 \right)$-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 $$λ_1+\dots+λ_α\ge -αθ(n,α)\barλ,\; α\le \frac{n}{2}$$ must have nonnegative constant holomorphic sectional curvature.

发表机构

• East China University of Technology（华东交通大学）
• Nanchang University（南昌大学）

机构由 AI 辅助整理，请以论文原文为准。