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The Möbius geometry ofwintgen ideal submanifolds

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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 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.

Original languageEnglish
Title of host publicationReal and Complex Submanifolds
EditorsHyunjin Lee, Jürgen Berndt, Yoshihiro Ohnita, Byung Hak Kim, Young Jin Suh
PublisherSpringer New York LLC
Pages411-425
Number of pages15
ISBN (Electronic)9784431552147
DOIs
StatePublished - 2014
Externally publishedYes
EventSatellite Conference on Real and Complex Submanifolds ICM 2014 with 18th International Workshop on Differential Geometry - Daejeon, Korea, Republic of
Duration: 10 Aug 201412 Aug 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume106
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceSatellite Conference on Real and Complex Submanifolds ICM 2014 with 18th International Workshop on Differential Geometry
Country/TerritoryKorea, Republic of
CityDaejeon
Period10/08/1412/08/14

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