Abstract
Some results on Ricci-symmetric contact metric manifolds are obtained. Second order parallel tensors and vector fields keeping curvature tensor invariant are characterized on a class of contact manifolds. Conformally flat contact manifolds are studied assuming certain curvature conditions. Finally some results onk-nullity distribution of contact manifolds are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BAIKOUSSIS, C., BLAIR, D. E. and KOUFOGIORGOS, T.: A decomposition of the curvature tensor of a contact manifold with ξ inN(k), Mathematics Technical Report, University of Ioannina (Greece), 1992.
BLAIR, D. E.: Contact manifolds in Riemannian geometry, Lecture notes in Math. 509, Springer-Verlag, Berlin, 1976.
BLAIR, D. E.: Two remarks on contact metric structures, Tôhoku Math. J. 29 (1977), 319–324.
BLAIR, D. E. and CHEN, H.: A classification of 3-dimensional contact metric manifolds withQϕ = ϕQ, II, Bull. Inst. Math. Acad. Sinica 20 (1992), 379–383.
BLAIR, D. E. and KOUFOGIORGOS, T.: When is the tangent sphere bundle conformally flat? To appear in Journal of Geometry.
BLAIR, D. E., KOUFOGIORGOS, T. and SHARMA, R.: A classification of 3-dimensional contact metric manifolds withQϕ = ϕQ, Kodai Math. J. 13 (1990), 391–401.
BLAIR, D. E. and PATNAIK, J. N.: Contact manifolds with characteristic vector field annihilated by the curvature, Bull. Inst. Math. Acad. Sinica 9 (1981), 533–545.
BLAIR, D. E. and SHARMA, R.: Three dimensional locally symmetric contact metric manifolds, Boll. U.M.I. (7)4-A (1990), 385–390.
BLAIR, D. E. and SIERRA, J. M.: 5-dimensional locally symmetric contact metric manifolds, To appear in Bol. U.M.I.
OKUMURA, M.: Some remarks on space with certain contact structures, Tôhoku Math. J. 14 (1962), 135–145.
PERRONE, D.: Contact Riemannian manifolds satisfyingR(X, ξ)R=0, Yokohama Math. J. 39 (1992), 141–149.
SHARMA, R.: Conformal and curvature symmetries of contact metric manifolds, C.R. Math. Rep. Acad. Sci. Canada 12 (1990), 235–240.
SHARMA, R.: Second order parallel tensors on contact manifolds II, C.R. Math. Rep. Acad. Sci. Canada 13 (1991), 259–264.
SHARMA, R. and KOUFOGIORGOS, T.: Locally symmetric and Ricci symmetric contact metric manifolds, Annals of global analysis and geometry 9 (1991), 177–182.
TANNO, S.: Locally symmetricK-contact Riemannian manifolds, Proc. Japan Acad. 43 (1967), 581–583.
TANNO, S.: Some differential equations on Riemannian manifolds, J. Math. Soc. Japan 30(1978), 509–531.
TANNO, S.: Ricci curvatures of contact Riemannian manifolds, Tôhoku Math. J. 40 (1988), 441–448.
TANNO, S.: Variational problems on contact metric manifolds, Trans. Amer. Math. Soc. 314 (1989), 349–379.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sharma, R. On the curvature of contact metric manifolds. J Geom 53, 179–190 (1995). https://doi.org/10.1007/BF01224050
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01224050