Advertisement

manuscripta mathematica

, Volume 93, Issue 1, pp 267–272 | Cite as

Extrinsic shape of circles and standard imbeddings of projective spaces

  • Toshiaki Adachi
  • Sadahiro Maeda
  • Koichi Ogiue
Article

Keywords

Projective Space Fundamental Form Isometric Immersion Complex Projective Space Holomorphie Sectional Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Adachi,Circles on a quaternionic space form, J. Math. Soc. Japan 48(1996), 205–227.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    T. Adachi,Kähler magnetic flows for a manifold of constant holomorphic sectional curvature, Tokyo J. Math. 18(1995), 473–483.zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    T. Adachi, S. Maeda and S. Udagawa,Circles in a complex projective space, Osaka J. Math. 32(1995), 709–719.zbMATHMathSciNetGoogle Scholar
  4. 4.
    B.-y. Chen and S. Maeda,Extrinsic characterizations of circles in a complex projective space imbedded in a Euclidean space, Tokyo J. Math. 19(1996), 169–185.zbMATHMathSciNetGoogle Scholar
  5. 5.
    D. Ferus,Immersions with parallel second fundamental form, Math. Z. 140(1974)87–92.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    D. Ferus,Symmetric submanifolds of Euclidean space, Math. Ann. 247(1980)81–93.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    S. Ishihara,Quaternion Kähler manifolds, J.Diff. Geom. 9(1974)483–500.zbMATHMathSciNetGoogle Scholar
  8. 8.
    S. Kobayashi and K. Nomizu,Foundations of differential geometry II, Interscience, New York, 1969.zbMATHGoogle Scholar
  9. 9.
    K. Nomizu and K. Yano,On circles and spheres in Riemannian geometry, Math. Ann. 210(1974) 163–170.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    B. O’Neill,Isotropic and Kaehler immersions, Canad. J. Math. 17(1965)905–915.MathSciNetGoogle Scholar
  11. 11.
    S.-s. Tai,Minimal imbedding of compact symmetric spaces of rank one, J. Diff. Geom. 2(1968)55–66.zbMATHMathSciNetGoogle Scholar
  12. 12.
    M. Takeuchi,Parallel submanifolds of space forms, Manifolds and Lie groups, in honor of Y. Matsushima, Birkhäuser, Boston, 1981, 429–447.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Toshiaki Adachi
    • 1
  • Sadahiro Maeda
    • 2
  • Koichi Ogiue
    • 3
  1. 1.Dept. of Math.Nagoya Institute of TechnologyNagoyaJapan
  2. 2.Dept. of Math.Shimane UniversityMatsueJapan
  3. 3.Dept. of Math.Tokyo Metropolitan UniversityTokyoJapan

Personalised recommendations