Research Article

On the Ricci Curvature of Normal-Metric Contact Pair Manifolds

Number: 34 March 30, 2021
EN

On the Ricci Curvature of Normal-Metric Contact Pair Manifolds

Abstract

In this study, we work on normal-metric contact pair manifolds under certain conditions related to the Ricci curvature. We obtain some results for generalized quasi-Einstein normal-metric contact pair manifolds. We prove that such manifolds are not pseudo-Ricci symmetric. Finally, we investigate Ricci solitons on normal-metric contact pair manifolds.

Keywords

Ricci symmetric, Normal-metric contact pair manifold, generalized quasi-Einstein, Ricci curvature

References

  1. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Springer Science Business Media, 2010.
  2. S. Kobayashi, Remarks on Complex Contact Manifolds, Proceedings of the American Mathematical Society 10 (1959) 164-167.
  3. S. Ishihara, M. Konishi, Complex Almost-contact Structures in a Complex Contact Manifold, Kodai Mathematical Journal 5 (1982) 30-37.
  4. B. Korkmaz, Normality of Complex Contact Manifolds, Rocky Mountain Journal of Mathematics 30 (2000) 1343-1380.
  5. A. T. Vanlı, D. E. Blair, The Boothby-Wang Fibration of the Iwasawa Manifold as a Critical Point of the Energy, Monatshefte für Mathematik 147 (2006) 75-84.
  6. A. T. Vanlı, İ. Ünal, Conformal, Concircular, Quasi-conformal and Conharmonic Flatness on Normal Complex Contact Metric Manifolds, International Journal of Geometric Methods in Modern Physics 14(05) (2017). doi: 10.1142/S0219887817500670
  7. A. T. Vanlı, İ. Ünal, I. On Complex \eta-Einstein Normal Complex Contact Metric Manifolds, Communications in Mathematics and Application 8(3) (2017) 301-313. doi:10.26713/cma.v8i3.509
  8. D. Fetcu, Harmonic Maps between Complex Sasakian Manifolds, Rendiconti del Seminario Matematico Universita e Politecnico di Torino 64 (2006) 319-329.
  9. B. J. Foreman, Complex Contact Manifolds and Hyperkahler Geometry, Kodai Mathematical Journal 23(1) (2000) 12-26.
  10. D. Fetcu, An Adapted Connection on a Strict Complex Contact Manifold, in Proceedings of the 5th Conference of Balkan Society of Geometers (2006) 54-61.
APA
Ünal, İ., & Sarı, R. (2021). On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. Journal of New Theory, 34, 115-122. https://izlik.org/JA35BB76LD
AMA
1.Ünal İ, Sarı R. On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. JNT. 2021;(34):115-122. https://izlik.org/JA35BB76LD
Chicago
Ünal, İnan, and Ramazan Sarı. 2021. “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”. Journal of New Theory, nos. 34: 115-22. https://izlik.org/JA35BB76LD.
EndNote
Ünal İ, Sarı R (March 1, 2021) On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. Journal of New Theory 34 115–122.
IEEE
[1]İ. Ünal and R. Sarı, “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”, JNT, no. 34, pp. 115–122, Mar. 2021, [Online]. Available: https://izlik.org/JA35BB76LD
ISNAD
Ünal, İnan - Sarı, Ramazan. “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”. Journal of New Theory. 34 (March 1, 2021): 115-122. https://izlik.org/JA35BB76LD.
JAMA
1.Ünal İ, Sarı R. On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. JNT. 2021;:115–122.
MLA
Ünal, İnan, and Ramazan Sarı. “On the Ricci Curvature of Normal-Metric Contact Pair Manifolds”. Journal of New Theory, no. 34, Mar. 2021, pp. 115-22, https://izlik.org/JA35BB76LD.
Vancouver
1.İnan Ünal, Ramazan Sarı. On the Ricci Curvature of Normal-Metric Contact Pair Manifolds. JNT [Internet]. 2021 Mar. 1;(34):115-22. Available from: https://izlik.org/JA35BB76LD