The Moebius geometry of Wintgen ideal submanifolds

Xiang Ma; Zhenxiao Xie

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arXiv · 1404.1440

The Moebius geometry of Wintgen ideal submanifolds

Xiang Ma·Zhenxiao Xie

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Abstract

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. They are Moebius invariant objects. The mean curvature sphere defines a conformal Gauss map into a Grassmann manifold. We show that any Wintgen ideal submanifold has a Riemannian submersion structure over a Riemann surface with the fibers being round spheres. Then the conformal Gauss map is shown to be a super-conformal and harmonic map from the underlying Riemann surface. Some of our previous results are surveyed in the final part.

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BibTeX RIS

Xiang Ma, Zhenxiao Xie. 2014-04-05. The Moebius geometry of Wintgen ideal submanifolds. https://arxiv.org/abs/1404.1440

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