Proceedings of the Japan Academy, Series A, Mathematical Sciences

A characterization of the second Veronese embedding into a complex projective space

Toshiaki Adachi and Sadahiro Maeda

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Abstract

We study curves of order 2 from the viewpoint of submanifold theory. We give a characterization of the parallel Kähler embeddings of a complex projective space into an ambient complex projective space from this point of view. This characterization is an improvement of the results in [N, PS].

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 7 (2001), 99-102.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393030

Digital Object Identifier
doi:10.3792/pjaa.77.99

Mathematical Reviews number (MathSciNet)
MR1857282

Zentralblatt MATH identifier
1038.53058

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

Keywords
Veronese embedding curves of order 2 complex projective spaces

Citation

Maeda, Sadahiro; Adachi, Toshiaki. A characterization of the second Veronese embedding into a complex projective space. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 7, 99--102. doi:10.3792/pjaa.77.99. https://projecteuclid.org/euclid.pja/1148393030


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References

  • Calabi, E.: Isometric imbedding of complex manifolds. Ann. Math., 269, 481–499 (1982).
  • Maeda, S., and Ohnita, Y.: Helical geodesic immersions into complex space forms. Geom. Dedicata, 30, 93–114 (1989).
  • Nomizu, K.: A characterization of the Veronese varieties. Nagoya Math. J., 60, 181–188 (1976).
  • Nakagawa, H., and Ogiue, K.: Complex space forms immersed in complex space forms. Trans. Amer. Math. Soc., 219, 289–297 (1976).
  • O'Neill, B.: Isotropic and Kaehler immersions. Canadian J. Math., 17, 907–915 (1965).
  • Pak, J. S., and Sakamoto, K.: Submanifolds with $d$-planar geodesic immersed in complex projective spaces. T$\hat{\mathrm{o}}$hoku Math. J., 38, 297–311 (1986).
  • Sakamoto, K.: Planar geodesic immersions. T$\hat{\mathrm{o}}$hoku Math. J., 29, 25–56 (1977).
  • Suizu, K., Maeda, S., and Adachi, T.: Characterization of totally geodesic Kähler immersions (preprint).