中文摘要：

在空间形式的 Submanifolds 满足著名 DDVV 不平等。在这不平等 pointwise 达到平等的 submanifold 被称为 Wintgen 理想的 submanifold。作为保角的不变的目标， Wintgen 理想的 submanifolds 用 M 的框架在这份报纸被调查 ? bius 几何学。我们分类尺寸 m 的 Wintgen 理想的 submanfiolds 3 并且任意的 codimension 什么时候照宗规地定义的 2-dimensional 分发 \(\mathbb { D }_2\) 是 integrable。如此的例子分别地在范围，欧几里德几何学的空格，或夸张空格在超级最小的表面上来自锥，柱体，或旋转 submanifolds。如果，我们推测那 \(\mathbb { D }_2\) 产生 k 维的 integrable 分发 \(\mathbb { D }_k\) 并且 k m，那么类似的减小定理适用。这归纳什么时候 3 在这份报纸被证明了的 k = 。

英文摘要：

Submanifolds in space forms satisfy the well-known DDVV inequality. A submanifold attaining equality in this inequality pointwise is called a Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are investigated in this paper using the framework of MSbius geometry. We classify Wintgen ideal submanfiolds of dimension rn ≥ 3 and arbitrary codimension when a canonically defined 2-dimensional distribution D2 is integrable. Such examples come from cones, cylinders, or rotational submanifolds over super-minimal surfaces in spheres, Euclidean spaces, or hyperbolic spaces, respectively. We conjecture that if D2 generates a k-dimensional integrable distribution Dk and k 〈 m, then similar reduction theorem holds true. This generalization when k = 3 has been proved in this paper.