论文标题
HOPF的曲折结构在复杂的双曲线空间中
A Twistor Construction of Hopf Real Hypersurfaces in Complex hyperbolic Space
论文作者
论文摘要
众所周知，复杂的投影空间中的HOPF真实的曲面可以在局部表征为复杂的子延伸物上的试管。对于某些但不是全部，在复杂双曲线空间中的Hopf真实曲面也是如此。本文的主要目的是以统一的方式展示如何在复杂双曲线空间中构建Hopf真实的曲面，从水平submanifold中的一个无限型$ 2 $ Plane Grassmannian的三个扭曲器空间之一，就自然的para para para-para-quaternionic quaternionickähhler结构而言。我们还在复杂双曲线空间中完全大地测量的复杂双曲线中的一组圆圈鉴定了这些扭曲的空间。作为应用程序，我们描述了所有经典的HOPF示例。我们还解决了复杂双曲空间中HOPF真正的超曲面存在的显着和长期存在的问题，与霍斯赛群不同，因此相关的主曲率为$ 2 $。我们展示了一种获取大量的方法。
It is very well known that Hopf real hypersurfaces in the complex projective space can be locally characterized as tubes over complex submanifolds. This also holds true for some, but not all, Hopf real hypersurfaces in the complex hyperbolic space. The main goal of this paper is to show, in a unified way, how to construct Hopf real hypersurfaces in the complex hyperbolic space from a horizontal submanifold in one of the three twistor spaces of the indefinite complex $2$-plane Grassmannian with respect to the natural para-quaternionic Kähler structure. We also identify these twistor spaces with the sets of circles in totally geodesic complex hyperbolic lines in the complex hyperbolic space. As an application, we describe all classical Hopf examples. We also solve the remarkable and long-standing problem of the existence of Hopf real hypersurfaces in the complex hyperbolic space, different from the horosphere, such that the associated principal curvature is $2$. We exhibit a method to obtain plenty of them.
