Springer Nature is making SARS-CoV-2 and COVID-19 research free View research | View latest news | Sign up for updates

Planar geodesic submanifolds in a quaternionic projective space

  • 29 Accesses


The planar geodesic submanifolds of a quaternionic projective space are studied. Especially, these submanifolds which are totally real or quaternionic CR-submanifolds are completely classified. Also, the non-existence of a planar geodesic, proper QR-product in a quaternionic projective space is proved.

This is a preview of subscription content, log in to check access.


  1. 1.

    Barros, M., Chen, B. Y. and Urbano, F., ‘Quaternion CR-Submanifolds of Quaternion Manifolds’, Kodai Math. J. 4 (1981), 399–417.

  2. 2.

    Chen, B. Y., ‘Totally Umbilical Submanifolds of Quaternion Space Form’, J. Austral. Math. Soc. (Series A) 26 (1978), 154–164.

  3. 3.

    Funabashi, S., ‘Totally Real Submanifolds of a Quaternionic Kaehlerian Manifold, Kòdai Math. Sem. Rep. 29 (1978), 261–270.

  4. 4.

    Funabashi, S., ‘Totally Complex Submanifolds of a Quaternionic Kaehlerian Manifold, Kodai Math. J. 2 (1979), 314–336.

  5. 5.

    Ishihara, S., ‘Quaternionic Kaehlerian Manifolds’, J. Diff. Geom. 9 (1974), 483–500.

  6. 6.

    Maeda, S. and Sato, N., ‘On Submanifolds All of Whose Geodesics are Circles in a Complex Space Form, Kodai Math. J. 6 (1983), 157–166.

  7. 7.

    Nomizu, K. and Yano, K., ‘On Circles and Spheres in Riemannian Geometry’, Math. Ann. 210 (1974), 163–170.

  8. 8.

    Ogiue, K., ‘On Kaehler Immersions’, Can. J. Math. 24 (1972), 1178–1182.

  9. 9.

    O'Neil, B., ‘Isotropic and Kaehler Immersions’, Can. J. Math. 17 (1965), 907–915.

  10. 10.

    Pak, J. S. ‘Planar Geodesic Submanifolds in Complex Space Forms’, Kodai Math. J. 1 (1978), 187–196.

  11. 11.

    Pak, J. S. and Sakamoto, K., ‘Submanifolds with Proper d-Planar Geodesic Immersed in Complex Projective Spaces’ (accepted in Tohoku Math. J.).

  12. 12.

    Pak, J. S. and Kang, T. H., ‘CR-Submanifolds with Cubic Geodesic Immersion in a Complex Space Form’ (accepted in Toyama Math. Rep.).

  13. 13.

    Sakamoto, K., ‘Planar Geodesic Immersions’, Tohoku Math. J. 29 (1977), 25–56.

  14. 14.

    Wolf, J. A., ‘Elliptic Space in Grassmann Manifolds’, Illinois J. Math. 7 (1963), 447–462.

Download references

Author information

Additional information

Research supported in part by a grant from KOSEF.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pak, J.S., Kang, T.H. Planar geodesic submanifolds in a quaternionic projective space. Geom Dedicata 26, 139–155 (1988). https://doi.org/10.1007/BF00151666

Download citation


  • Projective Space
  • Geodesic Submanifolds
  • Quaternionic Projective Space