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Wintgen ideal submanifolds with vanishing Möbius form

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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 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.

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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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  1. Department of Mathematics, China University of Mining and Technology (Beijing), Beijing, 100083, People’s Republic of China

    Zhenxiao Xie

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  1. Zhenxiao Xie
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Xie, Z. Wintgen ideal submanifolds with vanishing Möbius form. Ann Glob Anal Geom 48, 331–343 (2015). https://doi.org/10.1007/s10455-015-9473-1

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  • DOI: https://doi.org/10.1007/s10455-015-9473-1

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