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arXiv · 1402.3440

Moebius geometry of three dimensional Wintgen ideal submanifolds in S^5

Zhenxiao Xie·Tongzhu Li·Xiang Ma·Changping Wang
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Abstract

Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the normal scalar curvature. This property is conformal invariant; hence we study them in the framework of Moebius geometry, and restrict to three dimensional Wintgen ideal submanifolds in S^5. In particular we give Moebius characterizations for minimal ones among them, which are also known as (3-dimensional) austere submanifolds (in 5-dimensional space forms).

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Zhenxiao Xie, Tongzhu Li, Xiang Ma, Changping Wang. 2014-02-14. Moebius geometry of three dimensional Wintgen ideal submanifolds in S^5. https://doi.org/10.1007/s11425-013-4664-3

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