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

Ahmet Yıldız; Bilal Eftal Acet

Research Article

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

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

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

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).

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

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

Ahmet Yıldız Bilal Eftal Acet

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).

There are 11 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Research Article
Authors	Ahmet Yıldız This is me Bilal Eftal Acet This is me
Publication Date	August 15, 2009
Published in Issue	Year 2009 Issue: 019

Cite

APA	Yıldız, A., & Acet, B. E. (2009). ON WEAK SYMMETRIES OF (k, μ)– CONTACT METRIC MANIFOLDS. Journal of Science and Technology of Dumlupınar University(019), 41-46.