论文标题
Kähler歧管和第二类的曲率操作员
Kähler manifolds and the curvature operator of the second kind
论文作者
论文摘要
本文旨在研究Kähler歧管第二类的曲率操作员。第一个结果指出，$ \ frac {3} {2} {2}（m^2-1）$ - 非否（分别为$ \ frac {3} {3} {2}（M^2-1）$ - 非阳性）曲率操作员的第二种曲率（分别是不变的（$ frac）均不稳定性（分别），$ m $ m $二维的kähler歧管（分别为$ \ frac {2} {2} {2}（分别为$ \ frac {3} {3} {2} {2}（m^2-1）$ - 非阳性）曲率操作员的第二种曲率不变（均不是固定的（均不固定）。第二个结果断言，$ \左的$ M $二维Kähler歧管（\ frac {3m^3-m+2} {2m} {2m} \ right）$ - 第二类的正曲率操作员具有正相结合的双向曲率曲率，因此是Biholomorphic to Biholomorphic to Biholomorphic to $ \ $ \ $ \ $ \ $ \ $ {cp} cp} cp}^M {cp}^M.我们还证明了$ \ left（\ frac {3m^3+2m^2-3m-2} {2m} \ right）$ - 第二类的正曲率操作员意味着正交正交RICCI曲率。我们的方法是尖锐而代数。
This article aims to investigate the curvature operator of the second kind on Kähler manifolds. The first result states that an $m$-dimensional Kähler manifold with $\frac{3}{2}(m^2-1)$-nonnegative (respectively, $\frac{3}{2}(m^2-1)$-nonpositive) curvature operator of the second kind must have constant nonnegative (respectively, nonpositive) holomorphic sectional curvature. The second result asserts that a closed $m$-dimensional Kähler manifold with $\left(\frac{3m^3-m+2}{2m}\right)$-positive curvature operator of the second kind has positive orthogonal bisectional curvature, thus being biholomorphic to $\mathbb{CP}^m$. We also prove that $\left(\frac{3m^3+2m^2-3m-2}{2m}\right)$-positive curvature operator of the second kind implies positive orthogonal Ricci curvature. Our approach is pointwise and algebraic.
