Skip to main content
Log in

Locally symmetric and ricci-symmetric contact metric manifolds

  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

We have characterized locally symmetric and Ricci-symmetric contact metric manifolds of dimension greater than 3, by assuming certain conditions on the curvature and Ricci curvature along the characteristic vector field of the contact structure.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Blair, D.: Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509. Berlin-Heidelberg-New York: Springer-Verlag 1976.

    Google Scholar 

  2. Blair, D. E.: Two remarks on contact metric structures. Tôhoku Math. J.29 (1977), 319–324.

    Google Scholar 

  3. Blair, D. E.: When isT 1 M locally symmetric? Geometry & Topology. Singapore: World Sci. Publishing 1989, p. 15–30.

    Google Scholar 

  4. Blair, D. E. andPatnaik, J. N.: Contact manifolds with characteristic vector field annihilated by the curvature. Bull. Inst. Math. Acad. Sinica9 (1981), 533–545.

    Google Scholar 

  5. Blair, D. E. andSharma, R.: Three-dimensional locally symmetric contact metric manifolds. To appear in Boll. Un. Mat. Ital.

  6. Okumura, M.: Some remarks on space with certain contact structures. Tôhoku Math. J.14 (1962), 135–145.

    Google Scholar 

  7. Olszak, Z.: On contact metric manifolds. Tôhoku Math. J.31 (1979), 247–253.

    Google Scholar 

  8. Tanno, S.: Locally symmetricK-contact Riemannian manifolds. Proc. Japan. Acad.43 (1967), 581–583.

    Google Scholar 

  9. Tanno, S.: Ricci curvatures of contact Riemannian manifolds. Tôhoku Math. J.40 (1988), 441–448.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, R., Koufogiorgos, T. Locally symmetric and ricci-symmetric contact metric manifolds. Ann Glob Anal Geom 9, 177–182 (1991). https://doi.org/10.1007/BF00776855

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00776855

Keywords

Navigation