Möbius geometry of three-dimensional Wintgen ideal submanifolds in $\mathbb{S}^5 $

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 Möbius geometry, and restrict to three-dimensional Wintgen ideal submanifolds in S5. In particular, we give Möbius characterizations for minimal ones among them, which are also known as (3-dimensional) austere submanifolds (in 5-dimensional space forms).