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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
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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.

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

References

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