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Möbius geometry of three-dimensional Wintgen ideal submanifolds in \(\mathbb S^5\) - MaRDI portal

Möbius geometry of three-dimensional Wintgen ideal submanifolds in \(\mathbb S^5\) (Q477065)

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Möbius geometry of three-dimensional Wintgen ideal submanifolds in \(\mathbb S^5\)
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    Möbius geometry of three-dimensional Wintgen ideal submanifolds in \(\mathbb S^5\) (English)
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    2 December 2014
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    Submanifolds in space forms satisfy the well-known DDVV inequality \(s \leq c + \| H\|^2-s_N\), where \(s\) is the normalized scalar curvature, \(H\) is the mean curvature and \(s_N\) is the normal scalar curvature with respect to the induced metric of the submanifold. 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 Möbius geometry and the authors give Möbius characterizations for minimal three-dimensional Wintgen ideal submanifolds in \(\mathbb S^5\), which are known as austere submanifolds.
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    Wintgen ideal submanifolds
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    DDVV inequality
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    Möbius geometry
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    austere submanifolds
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    complex curves
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