ON WEAK SYMMETRIES OF (k, μ)– CONTACT METRIC MANIFOLDS

Year 2009, Issue: 019, 41 - 46, 15.08.2009

Ahmet Yıldız Bilal Eftal Acet

Abstract

In this study,
we consider weakly symmetric and weakly Ricci-symmetric (k, μ)-contact metric manifolds. We find necessary
conditions in order that a (k, μ)-contact
metric manifold be weakly symmetric and weakly Ricci symmetric.

Keywords

Weakly symmetric, weakly Ricci-symmetric, (k, μ)-contact metric manifolds

(k, μ)–DEĞME METRİK MANİFOLDLARIN ZAYIF SİMETRİLERİ ÜZERİNE

Abstract

Bu
çalışmada, zayıf simetrik ve zayıf Ricci-simetrik (k, μ)-değme metrik manifoldları göz önüne aldık. (k, μ)-değme metrik manifoldların zayıf
simetrik ve zayıf Ricci-simetrik olması için gerekli şartları bulduk.

Keywords

Zayıf simetrik, zayıf Ricci-simetrik, (k, μ)-değme metrik manifoldlar

References

• [1] Arslan K., Murathan C., Özgür C.and Yıldız A., “Pseudosymmetric contact metric manifolds in the sense of M.C.Chaki”, Proc.Estonian Acad. Sci. Phys. Math., 50, 1-9 (2001).
• [2] Blair D.E., “Contact manifolds in Riemannian geometry”, Lectures Notes in Mathematics 509, Springer-Verlag, Berlin, 146p, (1976).
• [3] Blair D.E., Koufogiorgos T., Papantoniou B.J., “Contact metric manifolds satisfying a nullity condition”, Israel Journal of Math., 91, 189-214 (1995).
• [4] Chaki M.C., “On pseudosymmetric manifolds”, An. Stiint. Univ. "A1. I. Cuza" Iasi Sect. I. a Mat., 33, 53-58 (1987).
• [5] Chaki M.C., “On pseudo Ricci-symmetric manifolds”, Bulgar J. Phys., 15, 526-531 (1988).
• [6] De U. C. and Bandyopadhyay S., “On weakly symmetric spaces”, Publ. Math. Debrecen, 54, 377-381 (1999).
• [7] De U. C., Binh T. Q., and Shaikh A. A., “On weakly symmetric and weakly Ricci-symmetric K-contact manifolds”, Acta Mathematica Academiae Paedagogicae Nyıreghaziensis, 16, 65-71 (2000).
• [8] Sato I., “On a structure similar to almost contact structure”, Tensor N. S., 30, 219-224 (1976).
• [9] Sato I., “On a structure similar to almost contact structure II”, Tensor N. S., 31, 199-205 (1977).
• [10] Tamassy L. and Binh T. Q., “On weakly symmetric and weakly projective symmetric Riemannian manifolds”, Coll. Math. Soc. J. Bolyai, 56, 663-670 (1992).
• [11] Tamassy L. and Binh T. Q., “On weak symmetries of Einstein and Sasakian manifolds”, Tensor N. S., 53, 140-148 (1993).