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).
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Xie, Z., Li, T., Ma, X. et al. Möbius geometry of three-dimensional Wintgen ideal submanifolds in \(\mathbb{S}^5 \) . Sci. China Math. 57, 1203–1220 (2014). https://doi.org/10.1007/s11425-013-4664-3
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DOI: https://doi.org/10.1007/s11425-013-4664-3