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Annals of Global Analysis and Geometry

, Volume 48, Issue 4, pp 331–343 | Cite as

Wintgen ideal submanifolds with vanishing Möbius form

  • Zhenxiao XieEmail author
Article

Abstract

Wintgen ideal submanifolds in space forms are those ones attaining equality pointwise in the so-called DDVV inequality which relates to the scalar curvature, the mean curvature and the scalar normal curvature. They are conformal invariant objects and hence can be studied in the framework of Möbius geometry. In this paper, we discuss Wintgen ideal submanifolds with vanishing Möbius form. In particular, for those ones with codimension 2, we can give a complete classification.

Keywords

Wintgen ideal submanifolds DDVV inequality Möbius form 

Mathematics Subject Classification

53A30 53A55 53C42 

Notes

Acknowledgments

This work is supported by the Fundamental Research Funds for the Central Universities.The author would like to thank Prof. C. P. Wang, Prof. X. Ma and Prof. T. Z. Li for many helpful discussions on Wintgen ideal submanifolds in the past two years. Finally, I am grateful to the referees for their critical viewpoints and suggestions, which improve the exposition and correct many errors.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of MathematicsChina University of Mining and Technology (Beijing)BeijingPeople’s Republic of China

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