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ON A CLASS OF GENERALIZED (k, μ)-CONTACT METRIC MANIFOLDS

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The object of the present paper is to study 3-dimensional generalized (k, μ)-contact metric manifolds with harmonic curvature tensor. Also locally Φ-Ricci symmetric and locally Φ-conharmonically symmetric 3-dimensional generalized (k, μ)-contact manifolds have been considered. An example of a locally Φ-conharmonically symmetric three dimensional generalized (k, μ)-contact manifold has been given.

Abstract

The object of the present paper is to study 3-dimensional generalized (k, μ)-contact metric manifolds with harmonic curvature tensor. Also locally Φ-Ricci symmetric and locally Φ-conharmonically symmetric 3-dimensional generalized (k, μ)-contact manifolds have been considered. An example of a locally Φ-conharmonically symmetric three dimensional generalized (k, μ)-contact manifold has been given.

참고문헌 (14)

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  2. Blair, D. E., "Contact manifolds in Riemannian geometry", 통권 : 509 (1976), Springer-Verlag
  3. Blair, D. E., "Two remarks on contact metric structures", Tohoku. Math. J, 29(3), pp.319~324 (1977)
  4. Boeckx, E., "A full classification of contact metric (k, μ)−spaces", Illinois J. Math, 44(1), pp.212~219 (2000)
  5. Baishya, K. K., "On Φ-recurrent generalized (k, μ)-contact metric manifolds", Lobachevskii J. Math., 27, pp.91~113 (2007)
  6. Baikoussis, C., "On a type of contact manifolds", J. of Geometry, 46, pp.1~9 (1993)
  7. U. C. De, "On -Ricci symmetric Sasakian manifolds", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 11(1), pp.47~52 (2008), 장전수학회
  8. Ghosh, S., "On Φ − Ricci symmetric (k, μ)", contact metric manifolds
  9. Gouli-Andreou, F., "A class of contact metric 3−manifolds with ξ 2 N(k, μ) and k, μ functions", Algebras, Groups and Geom., 17, pp.401~407 (2000)
  10. Jun, J. B., "On 3−dimensional almost contact metric manifolds", Kyungpook Math. J., 34(2), pp.293~301 (1994)
  11. Koufogiorgos, T., "On the existence of new class of contact metric manifolds", Canad. Math. Bull, 20(25), pp.1~8 (2000)
  12. Papantoniou, B. J., "Contact Riemannian manifolds satisfying R(ξ,X).R = 0 and ξ 2 (k, μ) − nullity distribution", Yokohama Math. J, 40(2), pp.149~161 (1993)
  13. Papantoniou, B. J., "Contact manifolds, harmonic curvature tensor, and (k, μ) − nullity distribution", Comment Math. Univ. Carolinne, 34(2), pp.323~334 (1993)
  14. Takahashi, T., "Sasakian Φ − symmetric spaces", Tohoku Math. J., 29, pp.91~113 (1977)

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