Skip to main content
Log in

A rigidity theorem for submanifolds with parallel mean curvature in a sphere

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. S. S.Chern, M.Do Carmo and S.Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length. In: Functional analysis and related fields. Berlin-Heidelberg-New York 1970.

  2. A. M. Li andJ. M. Li, An intrinsic rigidity theorem for minimal submanifolds in a sphere. Arch. Math.58, 582–594 (1992).

    Google Scholar 

  3. M. Okumura, Hypersurfaces and a pinching problem on the second fundamental tensor. Amer. J. Math.96, 207–213 (1974).

    Google Scholar 

  4. M. Okumura, Submanifolds and a pinching problem on the second fundamental tensor. Trans. Amer. Math. Soc.178, 285–291 (1973).

    Google Scholar 

  5. H. W. Xu, A pinching constant of Simons' type and isometric immersion. Chinese Ann. Math. Ser. A12, 261–269 (1991).

    Google Scholar 

  6. S. T. Yau, Submanifolds with constant mean curvature I, II. Amer. J. Math.96, 346–366 (1974);97, 76–100 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research partially supported by the National Natural Science Foundation of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, HW. A rigidity theorem for submanifolds with parallel mean curvature in a sphere. Arch. Math 61, 489–496 (1993). https://doi.org/10.1007/BF01207549

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01207549

Keywords

Navigation