Skip to main content Accessibility help
×
Home

REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE

  • SADAHIRO MAEDA (a1) and HIROO NAITOH (a2)

Abstract

We characterize real hypersurfaces of type (A) and ruled real hypersurfaces in a complex projective space in terms of two φ-invariances of their shape operators, and give geometric meanings of these real hypersurfaces by observing their some geodesics.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE
      Available formats
      ×

Copyright

References

Hide All
1.Adachi, T. and Maeda, S., A congruence theorem of geodesics on some naturally reductive Riemannian homogeneous manifolds, C. R. Math. Rep. Acad. Sci. Canada 26 (2004), 1117.
2.Adachi, T., Maeda, S. and Yamagishi, M., Length spectrum of geodesic spheres in a non-flat complex space form, J. Math. Soc. Japan 54 (2002), 373408.
3.Ferus, D., Symmetric submanifolds of Euclidean space, Math. Ann. 247 (1980), 8193.
4.Kimura, M., Sectional curvatures of holomorphic planes on a real hypersurface in Pn(ℂ), Math. Ann. 276 (1987), 487497.
5.Kimura, M. and Maeda, S., On real hypersurfaces of a complex projective space, Math. Z. 202 (1989), 299311.
6.Kobayashi, S. and Nagano, T., On filtered Lie algebras and geometric structures I, J. Math. Mech. 13 (1964), 875907.
7.Maeda, S. and Adachi, T., Integral curves of characteristic vector fields of real hypersurfaces in nonflat complex space forms, Geom. Dedicata 123 (2006), 6572.
8.Maeda, S. and Adachi, T., Extrinsic geodesics and hypersurfaces of type (A) in a complex projective space, Tohoku Math. J. 60 (2008), 597605.
9.Naitoh, H., Grassmann geometries on compact symmetric spaces of general type, J. Math. Soc. Japan 50 (3) (1998), 557–592.
10.Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms, in: Tight and Taut submanifolds (Cecil, T. E. and Chern, S. S., Editors) (Cambridge University Press, 1998), 233305.
11.Naitoh, H. and Takeuchi, M., Symmetric submanifolds of symmetric spaces, Sugaku Expositions 2 (2) (1989), 157188.

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed