Proceedings of the Japan Academy, Series A, Mathematical Sciences

Characterizations of space forms by circles on their geodesic spheres

Toshiaki Adachi and Sadahiro Maeda

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Abstract

In this paper we characterize space forms by observing the extrinsic shape of circles on their geodesic spheres.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 7 (2002), 143-147.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392638

Digital Object Identifier
doi:10.3792/pjaa.78.143

Mathematical Reviews number (MathSciNet)
MR1930220

Zentralblatt MATH identifier
1030.53057

Subjects
Primary: 53B25: Local submanifolds [See also 53C40]
Secondary: 53C40: Global submanifolds [See also 53B25]

Keywords
Curves of order 2 plane curves geodesics circles geodesic spheres space forms

Citation

Adachi, Toshiaki; Maeda, Sadahiro. Characterizations of space forms by circles on their geodesic spheres. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 143--147. doi:10.3792/pjaa.78.143. https://projecteuclid.org/euclid.pja/1148392638


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References

  • Adachi, T., and Maeda, S.: Space forms from the viewpoint of their geodesic spheres. Bull. Austral. Math. Soc., 62, 205–210 (2000).
  • Adachi, T., Maeda, S., and Udagawa, S.: Circles in a complex projective space. Osaka J. Math., 32, 709–719 (1995).
  • Chen, B.-Y., and Vanhecke, L.: Differential geometry of geodesic spheres. J. Reine Angew. Math., 325, 28–67 (1981).