Some Symmetry Properties of Almost S-Manifolds

Yıl 2017, Cilt: 13 Sayı: 3, 657 - 664, 30.09.2017

Yavuz Selim Balkan Mehmet Zeki Sarikaya

https://doi.org/10.18466/cbayarfbe.339323

Öz

Manifold
theory is an important topic in differential geometry. Riemannian manifolds are
a wide class of differentiable manifolds. 
Riemannian manifolds consist of two fundamental class, as contact
manifolds and complex manifolds. The notion of globally framed metric



















-manifold is a generalization of these fundamental classes.
Almost

-manifolds which are globally framed metric

-manifold generalize some contact manifolds carrying their
dimension to

. On the other hand, classification is important for
Riemannian manifolds with respect to some intrinsic and extrinsic tools as well
as all sciences. Moreover, symmetric manifolds play an important role in
differential geometry. There are a lot of symmetry type for Riemannian
manifolds with respect to different arguments. Under these considerations,
in the present paper  we study some
symmetry conditions on almost

-manifolds. We investigate weak symmetries and

-symmetries of these type manifolds. We obtain some necessary
and sufficient conditions to characterize of their structures. Firstly, we prove that
the existence of weakly symmetric and weakly Ricci symmetric almost

-manifolds under some special conditions. Then, we show that
every

-symmetric almost

-manifold verifying the

-nullity distribution is an

-Einstein manifold of globally framed type. Finally, we get
some necessary and sufficient condition for a

-Ricci symmetric almost

-manifold verifying the

-nullity distribution to be an

-Einstein manifold of globally framed type.

Anahtar Kelimeler

-Einstein Manifold, -Ricci Symmetric Manifolds, Almost -Manifold, Globally Framed Metric -Manifold, -Structure, Weakly Symmetric Manifold

Kaynakça

• 1. Yano, K., On a structure satisfying , Tech-nical Report No. 12, University of Washington, USA, 1961.
• 2. Goldberg, S.I., Yano, K., Globally framed -manifolds, Illinois Journal of Mathematics, 1971, 15(3), 456-474.
• 3. Ishihara, S., Normal structure satisfying , Kodai Mathematical Seminar Reports, 1966, 18(1), 36-47. 4. Blair, D.E., Geometry of manifolds with structural group , Journal of Differential Geometry, 1970, 4(2), 155-157.
• 5. Goldberg, S.I., Yano, K., On normal globally framed -manifolds, Tohoku Mathematical Journal, 1970, 22, 362-370.
• 6. Vanzura, J., Almost -contact structures, Annali della Scuola Normale Superiore di Pisa Mathématiques, 1972, 26, 97-115.
• 7. Cabrerizo, J.L., Fernandez, L.M., Fernandez, M., The curvature tensor fields on -manifolds with complemented frames, Annals of the Alexandru Ioan Cuza University – Mathematics, 1990, 36, 151-161.
• 8. Duggal, K.L., Ianus, S., Pastore, A.M., Maps ınterchanging -structures and their harmonicity, Acta Applicandae Mathematicae, 2001, 67(1), 91-115.
• 9. Blair, D.E., Koufogiorgos, T., Papantoniou, B.J., Contact metric manifolds satisfying a nullity condition, Israel Journal of Mathe-matics, 1995, 91, 189-214.
• 10. Cappelletti-Montano, B., Di Terlizzi, L., -homothetic trans-formations for a generalization of contact metric manifolds, Bulle-tin of the Belgian Mathematical Society - Simon Stevin, 2007, 14, 277-289.
• 11. Takahashi, T., Sasakian -symmetric space, Tohoku Mathe-matical Journal, 1977, 29, 91-113.
• 12. Tamassy, L., Binh, T.Q., On weak symmetries of Einstein and Sasakian manifolds, Tensor N.S. 1993, 53, 140-148.
• 13. Tamassy, L., Binh, T.Q., On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloquium Mathe-matical Society Janos Bolyai, 1992, 56, 663-670.
• 14. Chaki, M.C., On pseudo Ricci-symmetric manifolds, Bulgarian Journal of Physics, 1988, 15, 526-531.
• 15. Dileo, G., Lotta, A., On the structure and symmetry properties of almost -manifolds, Geometriae Dedicata, 2005, 110, 191-211.