Wintgen ideal submanifolds: reduction theorems and a coarse classification

Zhenxiao Xie, Tongzhu Li, Xiang Ma*, Changping Wang

*此作品的通讯作者

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4 引用 (Scopus)

摘要

Wintgen ideal submanifolds in space forms are those ones attaining equality pointwise in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the scalar normal curvature. As conformal invariant objects, they are suitable to study in the framework of Möbius geometry. This paper continues our previous work in this program, showing that Wintgen ideal submanifolds can be divided into three classes: the reducible ones, the irreducible minimal ones in space forms (up to Möbius transformations), and the generic (irreducible) ones. The reducible Wintgen ideal submanifolds have a specific low-dimensional integrable distribution, which allows us to get the most general reduction theorem, saying that they are Möbius equivalent to cones, cylinders, or rotational surfaces generated by minimal Wintgen ideal submanifolds in lower-dimensional space forms.

源语言英语
页(从-至)377-403
页数27
期刊Annals of Global Analysis and Geometry
53
3
DOI
出版状态已出版 - 1 4月 2018

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Xie, Z., Li, T., Ma, X., & Wang, C. (2018). Wintgen ideal submanifolds: reduction theorems and a coarse classification. Annals of Global Analysis and Geometry, 53(3), 377-403. https://doi.org/10.1007/s10455-017-9581-1