Locally symmetric and ricci-symmetric contact metric manifolds
- 61 Downloads
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.
KeywordsVector Field Characteristic Vector Group Theory Contact Structure Characteristic Vector Field
Unable to display preview. Download preview PDF.
- Blair, D.: Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509. Berlin-Heidelberg-New York: Springer-Verlag 1976.Google Scholar
- Blair, D. E.: Two remarks on contact metric structures. Tôhoku Math. J.29 (1977), 319–324.Google Scholar
- Blair, D. E.: When isT 1 M locally symmetric? Geometry & Topology. Singapore: World Sci. Publishing 1989, p. 15–30.Google Scholar
- 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
- Blair, D. E. andSharma, R.: Three-dimensional locally symmetric contact metric manifolds. To appear in Boll. Un. Mat. Ital.Google Scholar
- Okumura, M.: Some remarks on space with certain contact structures. Tôhoku Math. J.14 (1962), 135–145.Google Scholar
- Olszak, Z.: On contact metric manifolds. Tôhoku Math. J.31 (1979), 247–253.Google Scholar
- Tanno, S.: Locally symmetricK-contact Riemannian manifolds. Proc. Japan. Acad.43 (1967), 581–583.Google Scholar
- Tanno, S.: Ricci curvatures of contact Riemannian manifolds. Tôhoku Math. J.40 (1988), 441–448.Google Scholar