Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T13:00:13.039Z Has data issue: false hasContentIssue false
  • English
  • Français

Families of congruent curves and applications

Part of: Classical differential geometry

Published online by Cambridge University Press:  26 February 2010

I. Papadoperakis
I. Papadoperakis
Affiliation:
Department of Mathematics, University of Crete, 71409 Heraklion, Crete, Greece. E-mail: [email protected]
Get access

Extract

In connection with the thesis of Ch. Charitos (1989), T. Hasanis posed the following question.

MSC classification

Secondary: 53A05: Surfaces in Euclidean space
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 241 - 252
Copyright
Copyright © University College London 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[A, S] Ahlfors, L. and Sario, L.. Riemann Surfaces, 2nd printing (corrected) (Princeton Univ. Press, Princeton, New Jersey, 1965).Google Scholar
[C, P] Charitos, C. and Pamfilos, P.. Surfaces with isometric geodesies. Proc. Edinburgh Math. Soc. (2), 34 (1991), 359–362.CrossRefGoogle Scholar
[C1] Charitos, C.. Hypersurfaces with Congruent Geodesies. Math. Nachr., 155 (1992), 221–229.CrossRefGoogle Scholar
[C2] Charitos, C.. Surfaces with congruent shadow-lines. Mathematika, 37 (1990), 43–58.CrossRefGoogle Scholar
[F, S] Ferus, D. and Schirrmacher, S.. Submanifolds in Euclidean Space with Simple Geodesies. Math. Ann., 260 (1982), 57–62.CrossRefGoogle Scholar
[G, H] Greenberg, G. and Harper, J.. Algebraic Topology (Addison-Wesley, 1981).Google Scholar
[K] Klingenberg, W.. Lectures on Closed Geodesies (Springer-Verlag, 1978).CrossRefGoogle Scholar
[Mo] Montejano, L.. Convex bodies with homothetic sections. Bull. London Math. Soc, 23 (1991), 381–386.CrossRefGoogle Scholar
[Mu] Munkres, J.. Obstruction to the smoothing of piecewise-differentiable homeomorphisms. Bull. Amer. Math. Soc, 65 (1959), 332–334.CrossRefGoogle Scholar
[N] O'Neill, B.. Isotropic and Käihler immersions. Canad. J. Math., 17 (1965), 353–364.Google Scholar
[Sü] Suss, W.. Kennzeichnende Eigenschaften der Kugel als Folgerung eines Brouwerschen Fixpunktsatzes. Comment. Math. Helvet., 20 (1947), 61–64.CrossRefGoogle Scholar
[Sa] Sakamoto, K.. Helical immersions into a Euclidean space. Michigan Math. J., 33 (1986).CrossRefGoogle Scholar
[Sc] Schneider, . Convex bodies with congruent sections. Bull. London Math. Soc, 12 (1980), 52–54.CrossRefGoogle Scholar
[Sp] Spivak, M.. Differential Geometry, vol. 4, Second Edition (Publish or Perish, 1979).Google Scholar
[T] Takeuchi, N.. A sphere as a surface which contains many circles. J. Geom., 24 (1985), 123–130.CrossRefGoogle Scholar
[W] Whitehead, G.. Elements of Homotopy Theory (Springer-Verlag, 1978).CrossRefGoogle Scholar