Generalized Quasi-Conformal Curvature Tensor On Normal Metric Contact Pairs

Yıl 2020, , 194 - 199, 31.12.2020

İnan Ünal

https://doi.org/10.29132/ijpas.803809

Öz

The aim of this paper is to examine normal metric contact pair (NMCP) manifolds under the flatness conditions on
generalized quasi-conformal (GQC) curvature tensor. It is interested to classify GQC-flat and GQC-Z-flat NMCP
manifolds. We prove that a GQC-flat NMCP manifold is a generalized quasi-Einstein (GQE) manifold and also, such
manifolds are the space of generalized quasi-constant curvature. Finally, we consider the sectional curvature of NMCP
manifolds under the flatness conditions of GQC curvature tensor.

Anahtar Kelimeler

Contact metric pair, generalized quasi-conformal curvature tensor, curvature properties

Kontakt Metrik Çiftler Üzerinde Genelleştirilmiş Quasi-Conformal Eğrilik Tensörü

Öz

Bu çalışmanın amacı, normal metrik kontakt çift (NMCP) manifoldlarını genelleştirilmiş quasi-conformal eğrilik
(GQC) tensörünün sıfırlık koşulları altında incelemektir. Bu kapsamda GQC-düz ve GQC-Z-düz NMCP manifoldları ile
ilgilenilmiştir. Bir GQC-düz manifoldun genelleştirilmiş yarı-Einstein (GQE) manifold olduğu ve bu çeşit manifoldların
genelleştirilmiş yarı-sabit eğriliğe sahip olduğu ispatlanmıştır. Son olarak, GQC eğrilik tensörünün düzlük şartları altında,
NMCP manifoldlarının kesitsel eğrilikleri ele alınmıştır.

Anahtar Kelimeler

Kontakt metrik çift,, eğrilik özellikleri,, genelleştirilmiş quasi-conformal eğrilik tensörü

Kaynakça

• Acet, B. E. 2018. A note on Ricci solitons on para-Sasakian manifolds. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 11.2 237-242.
• Baishya, K. K. and Chowdhury P.R., 2016. On generalized quasi-conformal N (k, µ)-manifolds. Commun. Korean Math. Soc 31.1 163-176.
• Baishya, K. K. and Chowdhury P.R., 2017 Kenmotsu manifolds equipped with generalized quasi-conformal curvature tensor. Global Journal of Pure and Applied Mathematics 13.6 : 2493-2502.
• Baishya, K. K. and Chowdhury P.R., 2017 Semi-symmetry type LP-Sasakian manifolds. Acta Mathematica Academiae Paedagogicae Nyregyhaziensis 33 (2017): 67-83.
• Baishya, K. K. 2017. Ricci solitons in Sasakian manifold. Afrika Matematika 28.7-8 : 1061-1066.
• Bande, G. and Hadjar, A. 2005. Contact pairs Tohoku Mathematical Journal, Second Series, 57(2), 247-260.
• Bande, G. and Hadjar, A. 2009. Contact pair structures and associated metrics In Differential Geometry (pp. 266-275).
• Bande, G. and Hadjar, A. 2010. On normal contact pairs International Journal of Mathematics, 21(06), 737-754.
• Bande, G., Blair, D. E. and Hadjar, A. 2013. On the curvature of metric contact pairs Mediterranean journal of mathematics, 10(2), 989-1009.
• Bande, G., Blair, D.E. 2013. Symmetry in the geometry of metric contact pairs. Math. Nachr. 286, 1701–1709
• Bande, G., Blair, D. E. and Hadjar, A. 2015. Bochner and conformal flatness of normal metric contact pairs, Annals of Global Analysis and Geometry, 48(1), 47-56.
• Blair, D. E., Ludden G. D., and Yano, K. 1974. Geometry of complex manifolds similar to the Calabi-Eckmann manifolds Journal of Differential Geometry, 9(2), 263-274.
• De, U. C. and Ghosh, G. C., 2004. “On generalized quasi–Einstein manifolds”, Kyungpook Math. J. 44 , 607–615.
• Ünal, İ. 2020. Some flatness conditions on normal.metric.contact Pairs Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. 69(2): 262-271.
• Ünal, İ. 2020. Generalized Quasi-Einstein Manifolds in Contact Geometry. Mathematics, 8(9), 1592.
• Ünal, İ . 2020. On Metric Contact Pairs with Certain Semi-Symmetry Conditions. Politeknik Dergisi (In press)