Skip to main content
SpringerLink
Log in

A Characterization of Separable Hypersurfaces in Euclidean Space

  • Research Articles
  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

As generalizations of classical translation hypersurfaces, in this note we introduce the notion of separable hypersurfaces in an \((n+1)\)-dimensional Euclidean space. We give a complete classification of separable hypersurfaces with vanishing Gauss–Kronecker curvature.

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

  1. P. Dombrowski, “Krümmungsgrössen gleichungsdefinierter Untermannigfaltigkeiten Riemannscher Mannigfaltigkeiten,” Math. Nachr. 38, 133–180 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Hasanis and R. López, “Classification of separable surfaces with constant Gaussian curvature,” Manuscript Math. 166, 403–417 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Hasanis and R. López, “A characteristic property of Delaunay surfaces,” Proc. Amer. Math. Soc. 48, 5291–5298 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  4. S. Kaya and R. López, “Classification of zero mean curvature surfaces of separable type in Lorentz–Minkowski space,” Tohoku Math. J. 74, 263–286 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  5. H. L. Liu, “Translation surfaces with constant mean curvature in 3-dimensional spaces,” J. Geom. 64, 141–149 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  6. R. López and M. Moruz, “Translation and homothetical surfaces in Euclidean space with constant curvature,” J. Korean Math. Soc. 52, 523–535 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  7. H. F. Scherk, “Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen,” J. Reine Angew. Math. 13, 185–208 (1835).

    MathSciNet  MATH  Google Scholar 

  8. K. Seo, “Translation hypersurfaces with constant curvature in space forms,” Osaka J. Math. 50, 631–641 (2013).

    MathSciNet  MATH  Google Scholar 

  9. J. Weingarten, “Ueber die durch eine Gleichung der Form \(\mathfrak{X}+\mathfrak{Y}+\mathfrak{Z}=0\) darstellbaren Minimalflächen,” Nachr. Königl. Ges. d. Wissensch. Univ. Göttingen, 272–275 (1887).

    MATH  Google Scholar 

Download references

Funding

This work was supported by the General Project for Department of Liaoning Education (No. LN2020Q03) and (No. LJKMR20221583). All authors have made equal contributions.

Author information

Authors and Affiliations

  1. Trade Unions, Dongbei University of Finance and Economics, Dalian, 116025, China

    D. Chen

  2. Zanvyl Krieger School of Arts and Sciences, Johns Hopkins University, Baltimore, MD, 21218, United States

    C. X. Wang

  3. School of Investment Engineering Management, Dongbei University of Finance and Economics, Dalian, 116025, China

    X. S. Wang

Authors
  1. D. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. X. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X. S. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to D. Chen or X. S. Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, D., Wang, C.X. & Wang, X.S. A Characterization of Separable Hypersurfaces in Euclidean Space. Math Notes 113, 339–344 (2023). https://doi.org/10.1134/S0001434623030033

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434623030033

Keywords

Search

Navigation