The Möbius Geometry of Wintgen Ideal Submanifolds

  • Xiang Ma
  • Zhenxiao Xie
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


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 Möbius invariant objects. The mean curvature sphere defines a conformal Gauss map into a Grassmann manifold. We show that any Wintgen ideal submanifold of dimension greater than or equal to 3 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.


Riemann Surface Fundamental Form Curvature Vector Round Sphere Curvature Sphere 
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© Springer Japan 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingPeople’s Republic of China
  2. 2.Department of MathematicsChina University of Mining and Technology (Beijing)BeijingPeople’s Republic of China

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