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Journals / International Journal of Pure and Applied Sciences / 2020 / Cilt: 6 - Sayı: 2

Generalized Quasi-Conformal Curvature Tensor On Normal Metric Contact Pairs

Kontakt Metrik Çiftler Üzerinde Genelleştirilmiş Quasi-Conformal Eğrilik Tensörü

İnan ÜNAL
Pages
194–199
Publication Date
2022-10-19
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we consider the sectional curvature of NMCPmanifolds under the flatness conditions of GQC curvature tensor.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this paper is to examine normal metric contact pair (NMCP) manifolds under the flatness conditions ongeneralized quasi-conformal (GQC) curvature tensor.
📊
Key Findings & Data:It is interested to classify GQC-flat and GQC-Z-flat NMCPmanifolds.
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Conclusion & Impact:Finally, we consider the sectional curvature of NMCPmanifolds under the flatness conditions of GQC curvature tensor.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Kontakt metrik çift · eğrilik özellikleri · genelleştirilmiş quasi-conformal eğrilik tensörü

Abstract

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

Özet

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 ileilgilenilmiştir. Bir GQC-düz manifoldun genelleştirilmiş yarı-Einstein (GQE) manifold olduğu ve bu çeşit manifoldlarıngenelleştirilmiş yarı-sabit eğriliğe sahip olduğu ispatlanmıştır. Son olarak, GQC eğrilik tensörünün düzlük şartları altında,NMCP manifoldlarının kesitsel eğrilikleri ele alınmıştır.

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Cite This Article

ÜNAL, İ. (2022). Generalized Quasi-Conformal Curvature Tensor On Normal Metric Contact Pairs. International Journal of Pure and Applied Sciences, Cilt: 6 - Sayı: 2, 194–199. https://ajindex.com/articles/541569

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References (15)

  1. Acet, B. E. 2018. A note on Ricci solitons on para-Sasakian manifolds. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 11.2 237-242.
  2. Baishya, K. K. and Chowdhury P.R., 2016. On generalized quasi-conformal N (k, µ)-manifolds. Commun. Korean Math. Soc 31.1 163-176.
  3. 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.
  4. Baishya, K. K. and Chowdhury P.R., 2017 Semi-symmetry type LP-Sasakian manifolds. Acta Mathematica Academiae Paedagogicae Nyregyhaziensis 33 (2017): 67-83.
  5. Baishya, K. K. 2017. Ricci solitons in Sasakian manifold. Afrika Matematika 28.7-8: 1061-1066.
  6. Bande, G. and Hadjar, A. 2005. Contact pairs Tohoku Mathematical Journal, Second Series, 57(2), 247-260.
  7. Bande, G. and Hadjar, A. 2009. Contact pair structures and associated metrics In Differential Geometry (pp. 266-275).
  8. Bande, G. and Hadjar, A. 2010. On normal contact pairs International Journal of Mathematics, 21(06), 737-754.
  9. Bande, G., Blair, D. E. and Hadjar, A. 2013. On the curvature of metric contact pairs Mediterranean journal of mathematics, 10(2), 989-1009.
  10. Bande, G., Blair, D.E. 2013. Symmetry in the geometry of metric contact pairs. Math. Nachr. 286, 1701–1709
  11. 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.
  12. 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.
  13. De, U. C. and Ghosh, G. C., 2004. “On generalized quasi–Einstein manifolds”, Kyungpook Math. J. 44, 607–615.
  14. 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.
  15. 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)