STRUCTURE OF NEARLY α−COSYMPLECTIC MANIFOLDS

Abstract

The main purpose of this paper is to study the structure of nearly $\alpha -$ cosymplectic manifolds and some basic curvature relations of this manifolds satisfying some conditions where $\alpha $ is real defined.

Keywords

• Nearly cosymplectic manifolds
• nearly Kenmotsu manifolds
• nearly 􀀀cosymplectic manifolds

Kaynakça

1. [1]Blair DE, Goldberg SI. Topology of almost contact manifolds. Journal of Dierential Geometry 1967; 1: 347–354.
2. [2] Blair DE, Showers DK, Yano K. Nearly Sasakian structures. Kodai Mathematical Seminar Reports 1976; 27: 175–180. doi: 10.2996/kmj/1138847173
3. [3] Blair DE, Showers DK. Almost contact manifolds with killing structures tensors II. Journal of Dierential Geometry 1974; 9: 577–582.
4. [4] Gray A. Nearly Kaehler manifolds. Journal of Dierential Geometry 1970; 4(3): 283–309. doi: 10.4310/jdg/1214429504
5. [5] Gray A. The structure of nearly Kaehler manifolds. Mathematische Annalen 1976; 223(3): 233–248. doi: 10.1007/BF01360955
6. [6] Olszak Z. On almost cosymplectic manifolds. Kodai Mathematical Journal 1981; 4(2): 239–250. doi: 10.2996/kmj/1138036371
7. [7] Olszak Z. Nearly Sasakian manifolds 1979; 33(3): 277–286.
8. [8] Olszak Z. Five-dimensional nearly Sasakian manifolds 1980; 34(3): 273–276.

9. [9] Endo H. On Ricci curvatures of almost cosymplectic manifolds. Al. I. Cuza” Iasi sect. la Mat (N. S) 40 (1994): 75-83.
10. [10] Endo H. On the curvature tensor of nearly cosymplectic manifolds of constant -sectional curvature. Ann. St. Univ. Iasi 51 (2005):439-554.
11. [11] Shukla A. Nearly trans-Sasakian manifolds. Kuwait Journal of Science and Engineering 1996; 23(2).
12. [12] Behzad N, Niloufar HK.Onnearly Kenmotsu manifolds. Turkish Journal of Mathematics 2013; 37(25): 1040-1047. doi:10.3906/mat- 1207-38
13. [13] Kenmotsu K. A class of almost contact Riemannian manifold. Tohoku Mathematical Journal 1972; 24: 93–103.
14. [14] Goldberg SI, Yano K. Integrability of almost cosymplectic structures. Pasific Journal of Mathematics 1969; 31(2): 373–382. doi: 10.2140/pjm.1969.31.373
15. [15] Yano K, Kon M. Structures on manifolds, World Scientific,508p, 1984.
16. [16] Banaru M. On nearly-cosymplectic hypersurfaces in nearly-Kahlerian manifolds. Studia Universitatis BabeÅY¨ -Bolyai. Mathematica Cluj - Napoca 2002; 47(3): 2–11.
17. [17] Kirichenko VF. Almost cosymplectic manifolds satisfying the axiom of -holomorphic planes. Doklady Akademii Nauk SSSR 1983; 273(2): 280–284.
18. [18]Libermann MP. Sur les automorphismes infinitesimaux des structures symplectiques et des structures de contact . Colloque de Geometrie Dierentielle Globale Bruxelles,1958, Centre Belge de Recherche Mathematiques Louvain, 1959, pp. 37–59.
19. [19] Mobin A, Jun JB. On semi invariant submanifold of nearly Kenmotsu manifolds with quarter Journal of the Korean Society of Mathematical Education, The Pure and Applied Mathematics 2011; 18(1): 1–11. doi: 10.7468/jksmeb.2011.18.1.001
20. [20] De Nicola A , Dileo G, Yudin I. On Nearly Sasakian and nearly cosymplectic manifolds. Annali di Matematica 2018; 197: 127–138. doi: 10.1007/s10231-017-0671-2
21. [21] K˜A 1 4 peli EI, Piotr D, Murathan C. On the existence of proper nearly Kenmotsu manifolds. Mediterranean Journal of Mathematics 2016; 13: 4497–4507. doi: 10.1007/s00009-016-0758-91660-5446/16/064497-11
22. [22] Ozt˜A 1 4 rk H, Aktan N, Murathan C. Almost -cosymplectic (; ; )-spaces, arXiv:1007.0527. (or arXiv:1007.0527v1 [math.DG] for this version)
23. [23] Ayar G, Tekin P, Aktan N. Some curvature conditions on nearly cosymplectic manifolds. Indian Journal Of Industrial And Applied Mathematics 2019; 10(1): 51–58. doi: 10.5958/1945 919X.2019.00004.5
24. [24] Ayar G, Yıldırım M. Nearly cosymplectic manifolds with nullity conditions. Asian-European Journal of Mathematics 2019; 12(6): 2040012 (10 pages). doi: 10.1142/S1793557120400124
25. [25] Aktan N, Yıldırım M, Murathan C. Almost f-cosymplectic manifolds. Mediterranean Journal of Mathematics 2014; 11: 775–787. doi: 10.1007/s00009-013-0329-20378-620X/14/020775-13