Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-30T22:44:00.545Z Has data issue: false hasContentIssue false
  • English
  • Français

Classification of surfaces in three-sphere in Lie sphere geometry

Published online by Cambridge University Press:  22 January 2016

Takayoshi Yamazaki  and
Atsuko Yamada Yoshikawa
Takayoshi Yamazaki
Affiliation:
Sokahigashi High School, Kakinoki-cho 1110, Soka Saitama 340, Japan
Atsuko Yamada Yoshikawa
Affiliation:
Sokahigashi High School, Kakinoki-cho 1110, Soka Saitama 340, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We studied plane curves in Lie sphere geometry in [YY]. Especially we constructed Lie frames of curves in S2 and classified them by the Lie equivalence. In this paper we are concerned with surfaces in S3. We construct Lie frames and classify them. We moreover obtain the necessary and sufficient condition that two surfaces are Lie equivalent.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 143 , September 1996 , pp. 59 - 92
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

[C] Cecil, T. E., Lie sphere geometry, Springer-Verlag, New York, 1992.CrossRefGoogle Scholar
[CC] Cecil, T. E. and Chern, S. S., Tautness and Lie sphere geometry, Math. Ann., 278 (1987), 381–399.Google Scholar
[Gri] Griffiths, P., On Cartan’s method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry, Duke. Math. J., 41 (1974), 775–814.Google Scholar
[J] Jensen, G. R., Higher order contact of submanifolds of homogeneous spaces, Lecture Notes in Math., 610, Springer-Verlag, Berlin Heidelberg New York, 1977.Google Scholar
[M] Miyaoka, R., Lie contact structure and normal Cartan connections, Kodai. Math. J., 14 (1991), 13–41.Google Scholar
[P] Pinkall, U., Dupin hypersurfaces, Math., 270 (1985), 427–440.Google Scholar
[SY] Sato, H. and Yamaguchi, K., Lie contact manifolds, Geometry of manifolds (Shiohama, K. ed.) pp. 191 – 238, Academic Press, Boston, 1989.Google Scholar
[Y] Yamazaki, T., Dupin hypersurfaces and Lie sphere geometry, (in Japanese), Master thesis at Tôhoku University (1988).Google Scholar
[YY] Yamazaki, T. and Yoshikawa, A. Y., Plane curves in Lie sphere geometry, Kodai Math. J., to appear.Google Scholar