Skip to main content
SpringerLink
Log in

Characterization of spherical immersions of surfaces in R4

  • Published:
Bulletin of the Brazilian Mathematical Society, New Series Aims and scope Submit manuscript

Abstract

We obtain a characterization for spherical immersions in R4 in terms of local invariants. Besides the already known fact that the spherical immersions have to be semiumbilical, another condition among the Gauss curvature, the mean curvature and the resultant has to be satisfied.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. L. Bers. Riemann surfaces. New York University, Institute of Mathematical Sciences, (1958).

    MATH  Google Scholar 

  2. J. A. Little. On singularities of submanifolds of higher dimensional Euclidean spaces. Ann. Mat. Pura Appl. Series 4, 83(1) (1969), 261–335.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Monterde. Construction of non-hyperspherical immersions. Bull. Braz. Math. Soc. New Series, 43(2) (2012), 303–332.

    Article  MathSciNet  MATH  Google Scholar 

  4. S. M. Moraes and M. C. Romero-Fuster. Semiumbilics and 2-regular immersions of surfaces in euclidean spaces. Rocky Mountain J. Math., 35 (2005), 1327–1345.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Osserman. A survey on minimal surfaces. Dover Publications, New York (1986).

    MATH  Google Scholar 

  6. M. C. Romero-Fuster and F. Sánchez-Bringas. Umbilicity of surfaces with orthogonal asymptotic lines in R4. Differential Geom. Appl., 16(3) (2002), 213–224.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dpt. de Geometria i Topologia, Universitat de València, Avgda. Vicent Estellés, s/n, 46100, Burjassot, Spain

    J. Monterde & R. C. Volpe

Authors
  1. J. Monterde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. C. Volpe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Monterde.

Additional information

The first author is partially supported by grant MTM2012-33073 from the Spanish Ministry of Science and Innovation.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Monterde, J., Volpe, R.C. Characterization of spherical immersions of surfaces in R4 . Bull Braz Math Soc, New Series 47, 1037–1049 (2016). https://doi.org/10.1007/s00574-016-0202-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00574-016-0202-6

Keywords

Mathematical subject classification

Search

Navigation