Skip to main content
SpringerLink
Log in
Book cover

Global Differential Geometry and Global Analysis 1984 pp 227–239Cite as

Tight smoothing of some polyhedral surfaces

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1156))

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Apery, La surface de BOY, Thèse Univ. Louis Pasteur, Strasbourg 1984

    Google Scholar 

  2. T. F. Banchoff, Tightly embedded 2-dimensional polyhedral manifolds, Amer. J. of Math. 87, 462–472 (1965;Zbl. 136,210).

    Article  MathSciNet  MATH  Google Scholar 

  3. —, Critical points and curvature for embedded polyhedral surfaces, Amer. Math. Monthly 77, 475–485 (1970; Zbl. 191,528).

    Article  MathSciNet  MATH  Google Scholar 

  4. —, Non-rigidity theorems for tight polyhedra, Arch. Math. 21, 416–423 (1970; Zbl. 216,188).

    Article  MathSciNet  MATH  Google Scholar 

  5. T. F. Banchoff and N. H. Kuiper, Geometrical class and degree for surfaces in three-space, J. Diff. Geom. 16, 559–576 (1981; Zbl. 496.53003).

    MathSciNet  MATH  Google Scholar 

  6. W. Blaschke und K. Leichtweiβ, Elementare Differentialgeometrie, Springer 1973 (Grundlehren der mathematischen Wissenschaften Band 1) (1973; Zbl. 264.53001).

    Google Scholar 

  7. U. Brehm and W. Kühnel, Smooth approximation of polyhedral surfaces regarding curvatures, Geometriae Dedicata 12, 435–461 (1982), short version in: Proc. Conf. Global Diff. Geom. and Global Analysis, Berlin 1979, 64–68 (1981) (Lecture Notes in Mathematics Vol. 838)(Zbl. 437.53040 and 483.53046).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Császár, A polyhedron without diagonals, Acta Sci. Math. Szeged 13, 140–142 (1949; Zbl. 38,307).

    MathSciNet  MATH  Google Scholar 

  9. N. H. Kuiper, Convex immersions of closed surfaces in E3, Comment. Math. Helv. 35, 85–92 (1961; Zbl. 243.53043).

    Article  MathSciNet  MATH  Google Scholar 

  10. Tight topological embeddings of the Moebius band, J. Diff. Geom. 6, 271–283 (1972; Zbl. 234.53048).

    MathSciNet  MATH  Google Scholar 

  11. — Tight embeddings and maps, Submanifolds of geometrical class three in EN, Proc. Chern Symp. Berkeley 1979, 97–145, Springer (1980; Zbl. 461.53033).

    Google Scholar 

  12. — Geometry in total absolute curvature theory, in: Perspectives in Mathematics, Anniversary of Oberwolfach, 377–392, Birkhäuser 1984

    Google Scholar 

  13. U. Pinkall, Regular homotopy classes of tight surfaces (in preparation)

    Google Scholar 

  14. J. M. Wills, Reguläre polyedrische Mannigfaltigkeiten, Mitteilungen Math. Ges. Hamburg 11, 171–177 (1983).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik der TU Berlin, Str. d. 17. Juni 136, D - 1000, Berlin 12

    W. Kühnel

  2. Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, D - 5300, Bonn 3

    U. Pinkall

Authors
  1. W. Kühnel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. U. Pinkall
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Dirk Ferus Robert B. Gardner Sigurdur Helgason Udo Simon

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Kühnel, W., Pinkall, U. (1985). Tight smoothing of some polyhedral surfaces. In: Ferus, D., Gardner, R.B., Helgason, S., Simon, U. (eds) Global Differential Geometry and Global Analysis 1984. Lecture Notes in Mathematics, vol 1156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075095

Download citation

  • DOI: https://doi.org/10.1007/BFb0075095

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15994-0

  • Online ISBN: 978-3-540-39698-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation