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A complete classification of Blaschke parallel submanifolds with vanishing Möbius form

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Abstract

The Blaschke tensor and the Möbius form are two of the fundamental invariants in the Möbius geometry of submanifolds; an umbilic-free immersed submanifold in real space forms is called Blaschke parallel if its Blaschke tensor is parallel. We prove a theorem which, together with the known classification result for Möbius isotropic submanifolds, successfully establishes a complete classification of the Blaschke parallel submanifolds in Sn with vanishing Möbius form. Before doing so, a broad class of new examples of general codimensions is explicitly constructed.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11171091 and 11371018). The authors thank the referees for their helpful comments and suggestions.

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  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    XingXiao Li & HongRu Song

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  1. XingXiao Li
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  2. HongRu Song
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Correspondence to HongRu Song.

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Li, X., Song, H. A complete classification of Blaschke parallel submanifolds with vanishing Möbius form. Sci. China Math. 60, 1281–1310 (2017). https://doi.org/10.1007/s11425-016-0174-y

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