论文标题
Submanifolds在空间形式的产物中的旋转表示
Spinorial representation of submanifolds in a product of space forms
论文作者
论文摘要
我们提出了一种使浸入恒定曲率空间产物中的纺丝表征的方法。作为第一个应用，我们使用浸入式理论的基本定理的旋转器获得了证明。我们还研究特殊情况：我们恢复了先前已知的结果，这些结果是关于$ \ Mathbb {s}^2 \ times \ Mathbb {r} $，并且我们获得了沉浸式的新旋转特征，以$ \ Mathbb {s}^2 \ 2 \ 2 \ times \ times \ Mathbb {r}^2 $ and $ MATHBB {r MATHBBBB {r MATHBBBBBBBBBB}然后，我们在$ \ mathbb {h}^2 \ times \ mathbb {r} $中研究$ h = 1/2 $表面的理论，使用这种旋转方法，获得了一些基本结果的新证据，并与$ h = 1/2 $表面的理论直接与$ \ \ m m mathbbbbbb in of Mathbbbb Bbb Bbb {r}^r}^r}^$ {1,2}^$ {1,1,2}^^^^}
We present a method giving a spinorial characterization of an immersion in a product of spaces of constant curvature. As a first application we obtain a proof using spinors of the fundamental theorem of immersion theory in that spaces. We also study special cases: we recover previously known results concerning immersions in $\mathbb{S}^2\times\mathbb{R}$ and we obtain new spinorial characterizations of immersions in $\mathbb{S}^2\times\mathbb{R}^2$ and in $\mathbb{H}^2\times\mathbb{R}.$ We then study the theory of $H=1/2$ surfaces in $\mathbb{H}^2\times\mathbb{R}$ using this spinorial approach, obtain new proofs of some of its fundamental results and give a direct relation with the theory of $H=1/2$ surfaces in $\mathbb{R}^{1,2}.$
