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Classification of Moebius homogeneous Wintgen ideal submanifolds

2014/02/14 by Tongzhu Li, Li, Tongzhu, Xiang Ma +5
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Geometric Analysis and Curvature Flows #math.DG #msc:53A30 #msc:53A55

paper · pdf · doi:10.48550/arxiv.1402.3430

29 papers

arxiv created 2014/02/14 · arxiv updated 2014/02/17

Abstract

A submanifold in a real space form attaining equality in the DDVV inequality at every point is called a Wintgen ideal submanifold. They are invariant objects under the Moebius transformations. In this paper, we classify those Wintgen ideal submanifolds of dimension m>3 which are Moebius homogeneous. There are three classes of non-trivial examples, each related with a famous class of homogeneous minimal surfaces in Sn or CPn: the cones over the Veronese surfaces S2 in Sn, the cones over homogeneous flat minimal surfaces in Sn, and the Hopf bundle over the Veronese embeddings of CP1 in CPn.

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