ON $\alpha $-KENMOTSU MANIFOLDS SATISFYING SEMI-SYMMETRIC CONDITIONS

Yıl 2017, Cilt: 5 Sayı: 2, 192 - 206, 15.10.2017

Hakan Öztürk

Öz

The main purpose of this paper is to study $\alpha $-Kenmotsu manifolds satisfying some semi-symmetric conditions where $\alpha $ is a smooth function defined by $d\alpha \wedge \eta =0$ on $M^{2n+1}.$ In particularly, projectively, conformally and concircularly semi-symmetric tensor fields are considered. The results related to the effects of semi-symmetric conditions are given. Finally, illustrating examples on $\alpha $-Kenmotsu manifolds depending on $\alpha $ are constructed.

Anahtar Kelimeler

$\alpha $-Kenmotsu manifold, conformally flat, projectively flat

Kaynakça

• [1] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, Birkhauser, Boston, 2002.
• [2] J. B. Jun, U. C. De and G. Pathak, On Kenmotsu Manifolds, J. Korean Math. Soc., 42 (3)(2005), 435-445.
• [3] K. Kenmotsu, A Class of Contact Riemannian Manifold, Toh^oku Math. J., 24(1972), 93-103.
• [4] T. W. Kim, H. K. Pak, Canonical Foliations of Certain Classes of Amost Contact Metric Structures, Acta Math. Sinica, 21(4)(2005), 841-846.
• [5] K. Yano, M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3. World Scientic Publishing, Singapore, 1984.
• [6] Z. Olszak, On Amost Cosymplectic Manifolds, Kodai Math, 4 (2)(1981), 239-250.
• [7] H. Öztürk, N. Aktan and C. Murathan, On $\alpha$-Kenmotsu Manifolds Satisfying Certain Conditions, Applied Sciences, 12(2010), 115-126.
• [8] S. Tanno, The Automorphism Groups of Almost Contact Riemannian Manifolds, Tohoku Math. J., 21(1969), 21-38.
• [9] K. Nomizu, On Hypersurfaces Satisfying a Certain Condition on the Curvature Tensor, Tohoku Mat. J., 20(1968), 46-69.
• [10] Z. I. Szabo, Structure Theorem on Riemannian Spaces Satisfying R:R = 0, Journal of Differential Geo., 17(1982), 531-582.
• [11] Y. Ogawa, A Condition for a Compact Kaehlerian Space to be Locally Symmetric, Nat. Sci. Rep. Ochanomizu Univ., 28(1977), 21-23.
• [12] S. Tanno, Isometric Immersion of Sasakian Manifolds in Spheres, Kodai Math. Sem. Rep., 21(1969), 448-458.
• [13] H. Öztürk, N. Aktan, C. Murathan and A. T. Vanl, Almost $\alpha$-Cosymplectic $f$-Manifolds, The Journal of Alexandru Ioan Cuza University, 60 (1)(2014), 211-226.
• [14] N. Aktan, M. Yıldırım and C. Murathan, Almost $f$-Cosymplectic Manifolds, Mediterranean J. Math., 11(2014), 775-787.
• [15] C. S. Bagewadi, Venkatesha, Some Curvature Tensors on a Trans-Sasakian Manifold, Turkish J. Math., 31(2007), 111-121.
• [16] G. Calvaruso, D. Perrone, Semi-Symmetric Contact Metric Three-Manifolds, Yokohama Math. J., 49(2002), 149-161.
• [17] P. Dacko, Z. Olszak, On Conformally Flat Almost Cosymplectic Manifolds with Kaehlerian Leaves, Rend. Sem. Math. Univ. Pol. Torino, 56(1998), 89-103.
• [18] I. Vaisman, Conformal Changes of Almost Contact Metric Manifolds, Lecture Notes in Math., Berlin-Heidelberg-New York, 792(1980), 435-443.