Skip to main content
SpringerLink
Log in

Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space \({\mathbb{E}^4}\)

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper we study general rotational surfaces in \({\mathbb{E}^4}\) whose meridian curves lie in two-dimensional planes. We firstly find all minimal general rotational surfaces by solving the differential equation that characterizes minimal general rotational surfaces. Then we determine all pseudo-umbilical general rotational surfaces in \({\mathbb{E}^4}\).

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

Similar content being viewed by others

References

  • K. Arslan, B. K. Bayram, B. Bulca and G. Öztürk, Generalized rotation surfaces in \({\mathbb{E}^4}\) , Results Math. (2011), doi:10.1007/s00025-011-0103-3.

  • Cao X.F.: Pseudo-umbilical submanifolds of constant curvature Riemannian manifolds. Glasg. Math. J 43, 129–133 (2001)

    MathSciNet  MATH  Google Scholar 

  • : Pseudo-umbilical surfaces in Euclidean spaces. Kodai Math. J 23, 357–362 (1971)

    Article  MATH  Google Scholar 

  • Chen B.Y.: Pseudo-umbilical submanifolds of a Riemannian manifold of constant curvature II. J. Math. Soc. Japan 25, 105–114 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • Cole F.N., On rotations in space of four dimensions, Amer. J. Math. 12 (1890), 191–210

  • G. Ganchev and V. Milousheva, Minimal surfaces in the four-dimensional Euclidean space, preprint available at http://0806.3334v1.

  • Milousheva V.: General rotational surfaces in R 4 with meridians lying in twodimensional planes C. R. Acad. Bulgare Sci. 63, 339–348 (2010)

    MathSciNet  MATH  Google Scholar 

  • Moore C.L.E.: Surfaces of rotation in a space of four dimensions. Ann. of Math 21, 81–93 (1919)

    Article  MathSciNet  MATH  Google Scholar 

  • Vranceanu G.: Surfaces de rotation dans \({\mathbb{E}^4}\) . Rev. Roumaine Math. Pures Appl. 22, 857–862 (1977)

    MathSciNet  MATH  Google Scholar 

  • Yano K., Ishihara S.: Pseudo-umbilical submanifolds of codimension 2. Kodai Math. J. 21, 365–382 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  • Ying Y.L.: Pseudo-umbilical submanifolds in locally symmetric manifolds. J. Zhejiang Univ. Sci. Ed. 29, 130–134 (2002)

    MathSciNet  MATH  Google Scholar 

  • Xu Z.C., Xu S.L.: The pseudo-umbilical surfaces in R 4 and their Gauss maps. Chinese Quart. J. Math. 16, 46–51 (2001)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Ugˇur Dursun & Nurettin Cenk Turgay

Authors
  1. Ugˇur Dursun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nurettin Cenk Turgay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ugˇur Dursun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dursun, U., Turgay, N.C. Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space \({\mathbb{E}^4}\) . Mediterr. J. Math. 10, 497–506 (2013). https://doi.org/10.1007/s00009-011-0167-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-011-0167-z

Mathematics Subject Classification (2010)

Keywords

Search

Navigation