论文标题
真正双曲线空间的Kaehler子曼属
Kaehler submanifolds of the real hyperbolic space
论文作者
论文摘要
kaehler submanifolds的本地分类$ m^{2n} $的双曲空间$ \ mathbb {h}^{2n+p} $带有低的codimension $ 2 \ leq p \ leq p \ leq p \ leq n-1 $，仅在固有假设下仍然是一个广泛的开放问题。 The situation is quite different for submanifolds in the round sphere $\mathbb{S}^{2n+p}$, $2\leq p\leq n-1$, since Florit, Hui and Zheng have shown that the codimension has to be $p=n-1$ and then that any submanifold is just part of an extrinsic product of two-dimensional umbilical spheres in $ \ mathbb {s}^{3n-1} \ subset \ mathbb {r}^{3n} $。本文的主要结果是kaehler歧管的版本等于浸入球形亚策略的结果的双曲环境空间中。此外，我们概括了Dajczer和Vlachos获得的几个结果。
The local classification of Kaehler submanifolds $M^{2n}$ of the hyperbolic space $\mathbb{H}^{2n+p}$ with low codimension $2\leq p\leq n-1$ under only intrinsic assumptions remains a wide open problem. The situation is quite different for submanifolds in the round sphere $\mathbb{S}^{2n+p}$, $2\leq p\leq n-1$, since Florit, Hui and Zheng have shown that the codimension has to be $p=n-1$ and then that any submanifold is just part of an extrinsic product of two-dimensional umbilical spheres in $\mathbb{S}^{3n-1}\subset\mathbb{R}^{3n}$. The main result of this paper is a version for Kaehler manifolds isometrically immersed into the hyperbolic ambient space of the result for spherical submanifolds. Besides, we generalize several results obtained by Dajczer and Vlachos.
