Skip to main content
SpringerLink
Log in

Flat Möbius strips of given isotopy type in R 3 whose centerlines are geodesics or lines of curvature

  • Original Paper
  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We construct flat Möbius strips of arbitrary isotopy types, whose centerlines are geodesics or lines of 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. Chicone C. and Kalton N.J. (2002). Flat Embeddings of Möbius strip in R 3. Commun. Appl. Nonlinear Anal. 9: 31–50

    MathSciNet  MATH  Google Scholar 

  2. Murata, S., Umehara, M.: Flat Surfaces with singularities in Euclidean 3-space. preprint, math.DG/0605604

  3. Izumiya S. and Takeuchi N. (2004). New special curve and developable surface. Turk J. Math. 28: 153–163

    MathSciNet  MATH  Google Scholar 

  4. Randrup T. and Røgen P. (1996). Side of the Möbius strip. Arch. Math. 66: 511–521

    Article  MATH  Google Scholar 

  5. Randrup T. and Røgen P. (1997). How to twist a knot. Arch. Math 68: 252–264

    Article  MATH  Google Scholar 

  6. Røgen P. (2001). Embedding and knotting of flat compact surfaces in 3-space. Comment. Math. Helv. 76: 589–606

    Article  MathSciNet  Google Scholar 

  7. Schwarz G. (1990). The dark side of the Möbius strip. Am. Math. Monthly 97: 890–897

    Article  MATH  Google Scholar 

  8. Schwarz G. (1990). A pretender to the title “Canonical Möbius strip”. Pacific J. Math. 143: 195–200

    MathSciNet  MATH  Google Scholar 

  9. Wunderlich W. (1962). Über ein abwickelbares Möbiusband. Monatsh. Math. 66: 276–289

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan

    Yasuhiro Kurono & Masaaki Umehara

Authors
  1. Yasuhiro Kurono
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masaaki Umehara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masaaki Umehara.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kurono, Y., Umehara, M. Flat Möbius strips of given isotopy type in R 3 whose centerlines are geodesics or lines of curvature. Geom Dedicata 134, 109–130 (2008). https://doi.org/10.1007/s10711-008-9248-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10711-008-9248-y

Keywords

Mathematics Subject Classification (2000)

Search

Navigation