On M-projectively ϕ-symmetric (ϵ)-Kenmotsu manifolds

Öz

Locally and globally M-projectively ϕ-symmetric (ϵ)-Kenmotsu manifolds are studied. We show that a globally M-projectively ϕ-symmetric (ϵ)-Kenmotsu manifold is globally ϕ-symmetric. Some observations for a 3-dimensional locally M-projectively ϕ-symmetric (ϵ)-Kenmotsu manifold are given. We also give an example of a 3-dimensional locally M-projectively ϕ-symmetric (ϵ)-Kenmotsu manifold.

Anahtar Kelimeler

• (ϵ)-Kenmotsu manifold,3-dimensional (ϵ)-Kenmotsu manifolds,ϕ-symmetric,M-projective curvature tensor,Einstein manifold

Kaynakça

1. Bejancu A, Duggal KL. Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math & Math Sci., 16 (3), (1993), 545-556.
2. Blair DE, Koufogiorgos T, Sharma R. A classification of 3-dimensional contact metric manifolds with ϕQ=Qϕ, Kodai Math.J., 13 (3)(1990), 391-401.
3. Boeckx E, Buecken P, Vanhecke L. On ϕ-symmetric contact metric spaces, Glasgow Math.J., 41 (1999), 409-416.
4. De UC. On ϕ-symmetric Kenmotsu manifolds, Int. Electron. J. Geom., 1(1) (2008), 33-38.
5. De UC, Ozgur C, Mondal AK. On ϕ-quasiconformally symmetric Sasakian manifolds, Indag. Mathem., N.S., 20 (2), (2009), 191-200.
6. De UC, Sarkar A. On (ϵ)-Kenmotsu manifolds, Hadronic Jour., 32 (2009), 231-242.
7. Duggal KL. Space time manifold and contact structures, Int. J. Math & Math Sci., 13 (1990), 545-554.
8. Kenmotsu K. A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93 - 103.

9. Kumar R, Rani R, Nagaich RK. On sectional curvature of (ϵ)-Sasakian manifolds, Int. J. Math & Math. Sci., 2007 Artcle ID 93562, doi:10.1155/2007/93562.
10. Ojha RH. A note on the M-projective curvature tensor, Indian. J. Pure Appl. Math., 8, 12(1975), 1531-1534.
11. Ojha RH. M-projectively flat Sasakian manifolds, Indian. J. Pure Appl. Math., 17, 4 (1986), 481-484.
12. O’Neill B. Semi-Riemannian Geometry with Applications to relativity, Academic Press, New York, NY, USA, 1983.
13. Perktas SY, Kiliç E, Tripathi MM, Keleş S. On (ϵ)-para Sasakian 3-manifolds, Int. J. Pure Appl. Math., 77, 4 (2012), 485-499.
14. Pokhariyal GP, Mishra RS. Curvature tensor and their relativistic significance II, Yokohama Math. J., 19 (1971), 97-103.
15. Takahashi T. Sasakian manifold with pseudo-Riemannian metric, Tohoku Math. J., 21 (1969), 271-290.
16. Takahashi T. Sasakian ϕ-symmetric spaces, Tohoku Math. J., (2) 29(1)(1977), 91-113.
17. Xufeng X, Xiaoli C. Two theorems on (ϵ)-Sasakian manifolds, Int. J. Math & Math. Sci., 21 (2) (1998), 249-254.