Skip to main content
SpringerLink
Log in

On the Kenmotsu Hypersurfaces of Special Hermitian Manifolds

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We consider almost contact metric hypersurfaces of almost Hermitian manifolds of class W3 (in the Gray–Hervella terminology). We establish a criterion for minimality of such hypersurfaces in the case when the contact metric structure is cosymplectic.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arnol'd V. I., Mathematical Methods in Classical Mechanics [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  2. Hurt N. E., Geometric Quantization in Action [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  3. Kirichenko V. F., “Sur la gèomètrie des variètès approximativement cosymplectiques,” C. R. Acad. Sci. Paris Ser. I, 295,No. 12, 673-676 (1982).

    Google Scholar 

  4. Blair D. E., “Contact manifolds in Riemannian geometry,” Lecture Notes in Math., 509, 1-145 (1976).

  5. Kenmotsu K., “A class of almost contact Riemannian manifolds,” Tôhoku Math. J., 24, 93-103 (1972).

    Google Scholar 

  6. Kirichenko V. F., “On geometry of Kenmotsu manifolds,” Dokl. Ros. Akad. Nauk, 380,No. 5, 585-587 (2001).

    Google Scholar 

  7. Banaru M. B., “The type number of nearly cosymplectic hypersurfaces of nearly Kähler manifolds,” Fund. i Appl. Mat., 8,No. 2, 357-364 (2002).

    Google Scholar 

  8. Banaru M. B., “Some theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” Mat. Vesnik, 53, 103-110 (2001).

    Google Scholar 

  9. Gray A. and Hervella L. M., “The sixteen classes of almost Hermitian manifolds and their linear invariants,” Ann. Mat. Pura Appl., 123,No. 4, 35-58 (1980).

    Google Scholar 

  10. Kirichenko V. F., “Hermitian geometry of six-dimensional symmetric submanifolds of the Cayley algebra,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 3, 6-13 (1994).

  11. Arsen'eva O. E. and Kirichenko V. F., “Self-dual geometry of generalized Hermitian surfaces,” Mat. Sb., 189,No. 1, 21-44 (1998).

    Google Scholar 

  12. Banaru M. B., “Hermitian geometry of six-dimensional submanifolds of the Cayley algebra,” Mat. Sb., 193,No. 5, 3-16 (2002).

    Google Scholar 

  13. Norden A. P., The Theory of Surfaces [in Russian], GITTL, Moscow (1956).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Smolensk Humanitarian University, Russia

    M. B. Banaru

Authors
  1. M. B. Banaru
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banaru, M.B. On the Kenmotsu Hypersurfaces of Special Hermitian Manifolds. Siberian Mathematical Journal 45, 7–10 (2004). https://doi.org/10.1023/B:SIMJ.0000013009.33523.2b

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:SIMJ.0000013009.33523.2b

Search

Navigation