论文标题
Kähler歧管中的全态分段曲率和“凸”真实曲面
The holomorphic sectional curvature and "convex" real hypersurfaces in Kähler manifolds
论文作者
论文摘要
我们证明，严格的伪有孔的真实超曲面的田中 - 韦布斯特圆形截面曲率是“半度性地”沉浸在适当的凝聚力条件下的非阴性全态分段曲率的Kähler歧管中。这给出了Chanillo，Chiu和Yang提出的关于Tanaka-Webster标量曲率曲率的积极性的部分答案。 Chen，用于非负溶性截面曲率的Kähler歧管中的紧凑“凸”真实曲面。我们的方法非常简单，并使用高斯方程式的版本将伪雄杆菌歧管浸入Kähler歧管中。
We prove a sharp lower bound for the Tanaka-Webster holomorphic sectional curvature of strictly pseudoconvex real hypersurfaces that are "semi-isometrically" immersed in a Kähler manifold of nonnegative holomorphic sectional curvature under an appropriate convexity condition. This gives a partial answer to a question posed by Chanillo, Chiu, and Yang regarding the positivity of the Tanaka-Webster scalar curvature of the boundary of a strictly convex domain in $\mathbb{C}^2$ from 2012. In fact, the main result proves a stronger positivity property, namely the $\frac12$-positivity in the sense of Cao, Chang, and Chen, for compact "convex" real hypersurfaces in a Kähler manifold of nonnegative holomorphic sectional curvature. Our approach is rather simple and uses a version of the Gauss equation for semi-isometric CR immersions of pseudohermitian manifolds into Kähler manifolds.
