Skip to main content
SpringerLink
Log in

Width and breadth for convex bodies in Riemannian manifolds

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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

References

  1. A. D.Aleksandrov, Die innere Geometrie der konvexen Flächen. Berlin 1955.

  2. J. Bolton, Transnormal hypersurfaces. Proc. Cambridge Phil. Soc74, 43–48 (1973).

    Google Scholar 

  3. J. Bolton, Transnormal systems. Quart. J. Math. (2)24, 385–395 (1973).

    Google Scholar 

  4. Yu. D. Burago andV. A. Zalgaller, Convex sets in Riemannian spaces of non-negative curvature. Russian Math. Surveys (3)32, 1–57 (1977).

    Google Scholar 

  5. J. Cheeger andD. Gromoll, On the structure of complete manifolds of non-negative curvature. Ann. of Math. (3)96, 413–443 (1972).

    Google Scholar 

  6. B. V.Dekster, Bodies of constant width in Riemannian manifolds and spaces of constant curvature. In: “Victor Klee Festschrift”, Appl. Geometry and Discrete Math., the DIMACS series in Discrete Math. and Theoretical Computer Science, copublished by AMS and ACM4, 181–192 (1991).

  7. B. V. Dekster, In- and circumcenters of manifolds of constant width. Geom. Dedicata38, 67–71 (1991).

    Google Scholar 

  8. B. V.Dekster, Manifolds of constant width. Proc. Asian Math. Congress 1990, to appear.

  9. B. V.Dekster, Double normals characterize manifolds of constant width. Preprint.

  10. S. Nishikawa, Transnormal hypersurfaces — Generalized constant width for Riemannian manifolds. Tohoku Math. J.25, 451–459 (1973).

    Google Scholar 

  11. S. Nishikawa, Compact two-transnormal hypersurfaces in a space of constant curvature. J. Math. Soc. Japan, (4)26, 625–635 (1974).

    Google Scholar 

Download references

Author information

Author notes

  1. B. V. Dekster

    Present address: Mathematics Mount Allison University, E0A 3C0, Sackville, N. B., Canada

Authors and Affiliations

    Authors
    1. B. V. Dekster
      View author publications

      You can also search for this author in PubMed Google Scholar

    Additional information

    Supported by a Canadian NSERC Grant.

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Dekster, B.V. Width and breadth for convex bodies in Riemannian manifolds. Arch. Math 58, 190–198 (1992). https://doi.org/10.1007/BF01191885

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01191885

    Keywords

    Search

    Navigation