ON INVARIANT SUBMANIFOLDS OF ALMOST $\alpha$-COSYMPLECTIC $f$-MANIFOLDS

Year 2015, Volume: 3 Issue: 2, 245 - 253, 01.10.2015

Selahattin Beyendı , Nesip Aktan , Ali İhsan Sıvrıdağ

https://izlik.org/JA75KU67WW

Abstract

In this paper, we investigate some properties of invariant submanifolds of almost $\alpha$-cosymplectic f- manifolds. We show that every invariant submanifold of an almost $\alpha$-cosymplectic f- manifold with Kaehlerian leaves is also an almost $\alpha$-cosymplectic f- manifold with Kaehlerian leaves. Moreover, we give a theorem on minimal invariant submanifold and obtain a necessary condition on a invariant submanifold to be totally geodesic. Finally, we study some properties of the curvature tensors of M and fM.

Keywords

Almost -cosypmlectic f-manifold , invariant submanifold , semi parallel and 2-semi parallel submanifold

References

• [1] Arslan K., Lumiste C., Murathan C. and Ozgur C., 2- semiparallel Surfaces in Space Forms. I. Two Particular Cases, Proc. Estonian Acad. Sci Phys. Math., 49(3), (2000), 139-148.
• [2] Blair D.E., Geometry of manifolds with structural group U(n)  O(s), J. Dierential Geometry, 4(1970), 155-167.
• [3] Chen B.Y., Geometry of submanifolds, Marcel Dekker Inc., New York, (1973).
• [4] Chinea D., Prestelo P.S., Invariant submanifolds of a trans-Sasakian manifolds. Publ. Mat. Debrecen, 38/1-2 (1991), 103-109.
• [5] Endo H., Invariant submanifolds in contact metric manifolds, Tensor (N.S.) 43 (1) (1886), pp. 193-202.
• [6] Erken K.I, Dacko P. and Murathan C., Almost -paracosymplectic manifolds, arxiv: 1402.6930v1 [Math:DG] 27 Feb 2014.
• [7]  Ozturk H., Murathan C., Aktan N., Vanli A.T., Almost -cosymplectic f-manifolds Analele stntfce ale unverstat 'AI.I Cuza' D as (S.N.) Matematica, Tomul LX, f.1., (2014).
• [8] Kon M., Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep., 27, (1973), 330-336.
• [9] Terlizi L. D., On invariant submanifolds of C and S-manifolds. Acta Math. Hungar. 85(3), (1999), 229-239.
• [10] Sarkar A. and Sen M., On invariant submanifold of trans- sasakian manifolds, Proceedings of the Estonian Academy of Sciences, 61(1), (2012), 29-37.
• [11] De A., Totally geodesic submanifolds of a trans-Sasakian manifold, Proceedings of the Estonian Academy of Sciences, 62(4), (2013), 249-257.
• [12] Yano K. and Kon M., Structures on manifolds. World Scientic, Singapore (1984).
• [13] Yano K., On a structure dened by a tensor f of type (1; 1) satisfying '3 + ' = 0, tensor N S., 14, (1963), 99-109.