Skip to main content
SpringerLink
Log in
Book cover

Global Differential Geometry and Global Analysis pp 82–93Cite as

The bieberbach case in gromov’s almost flat manifold theorem

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 838))

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. Bieberbach, L., Ueber die Bewegungsgruppen der Euklidischen Räume, I: Math. Ann. 70 (1911) 297–336; II: Math. Ann. 72 (1912) 400–412.

    MathSciNet  MATH  Google Scholar 

  2. Buser, P., Karcher, H., Gromov’s almost flat manifold theorem (to appear).

    Google Scholar 

  3. Gromov, M., Almost flat manifolds, J. Differential Geometry 13 (1978) 231–241.

    MathSciNet  MATH  Google Scholar 

  4. Wolf, J., Spaces of constant curvature. McGraw Hill, New York (etc.) 1967.

    MATH  Google Scholar 

Other proofs of the Bieberbach theorem

  1. Auslander, L., Bieberbach’s theorems on space groups and discrete uniform subgroup of Lie groups I: Ann. of Math. 71 (1960) 579–590; Amer. J. Math. 83 (1961), 276–280.

    MathSciNet  MATH  Google Scholar 

  2. Frobenius, G. Über die unzerlegbaren diskreten Bewegungsgruppen, Sitz. ber. der Preuss. Akad. Wissen., Berlin, (1911), 654–665.

    MATH  Google Scholar 

  3. Zassenhaus, H., Beweis eines Satzes über diskrete Gruppen, Abh. Math. Sem. Univ. Hamburg, 12 (1938), 289–312.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Peter Buser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hermann Karcher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Dirk Ferus Wolfgang Kühnel Udo Simon Bernd Wegner

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Buser, P., Karcher, H. (1981). The bieberbach case in gromov’s almost flat manifold theorem. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088844

Download citation

  • DOI: https://doi.org/10.1007/BFb0088844

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10285-4

  • Online ISBN: 978-3-540-38419-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation