호남수학학술지 (Honam Mathematical Journal)

  • 제43권4호
  • /
  • Pages.701-715
  • /
  • 2021
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON THE ADAPTED CONNECTIONS ON KAEHLER-NORDEN SILVER MANIFOLDS

  • Mohammad, Sameer (Department of Mathematics, Jaypee University of Information Technology) ;
  • Pandey, Pradeep Kumar (Department of Mathematics, Jaypee University of Information Technology)
  • 투고 : 2021.08.08
  • 심사 : 2021.09.16
  • 발행 : 2021.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we study almost complex Norden Silver manifolds and Kaehler-Norden Silver manifolds. We define adapted connections of first, second and third type to an almost complex Norden Silver manifold and establish the necessary and sufficient conditions for the integrability of almost complex Norden Silver structure. Moreover, we investigate that a complex Norden Silver map is a harmonic map between Kaehler-Norden Silver manifolds.

키워드

참고문헌

  1. P. Baird and J. C. Wood, Harmonic Morphisms between Riemannian manifolds, Oxford University Press, London, 2003.
  2. L. Bilen, S. Turanli, and A. Gezer, On Kaehler-Norden-Codazzi Golden structures on pseudo-Riemannian manifolds, Int. J. Geom. Methods Mod. Phys., 15 (2018), 1-10.
  3. M. Crasmareanu and C. Hretcanu, Golden differential geometry, Chaos Solitons Fractals, 38 (5) (2008), 1229-1238. https://doi.org/10.1016/j.chaos.2008.04.007
  4. F. Etayo, R. Santamaria, and A. Upadhyay, On the geometry of almost Golden Riemannian manifolds, Mediterr. J. Math., 14 (2017), 1-14. https://doi.org/10.1007/s00009-016-0833-2
  5. A. Gezer and C. Karaman, Golden-Hessian structures, Proc. Natl. Acad. Sci. India Phys. Sci., 86 (2016), 41-46. https://doi.org/10.1007/s40010-015-0226-0
  6. A. Gezer, N. Cengiz, and A. Salimov, On integrability of Golden Riemannian structures, Turk. J. Math., 37 (2013), 693-703.
  7. S. I. Goldberg and K. Yano, Polynomial structures on manifolds, Kodai Math. Sem. Rep., 22 (1970), 199-218. https://doi.org/10.2996/kmj/1138846118
  8. C. Hretcanu and M. Crasmareanu, Applications of the Golden ratio on Riemannian manifolds, Turk. J. Math., 33 (2009), 179-191.
  9. M. Iscan and A. A. Salimov, On Kaehler-Norden manifolds, Proc. Indian Acad. Sci. Math. Sci., 119 (2009), 71-80. https://doi.org/10.1007/s12044-009-0008-1
  10. R. Kumar, G. Gupta, and R. Rani, Adapted connections on Kaehler-Norden Golden manifolds and harmonicity, Int. J. Geom. Methods Mod. Phys., 17 (2) (2019), 2050027-10. https://doi.org/10.1142/s0219887820500279
  11. M. Ozkan and B. Peltek, A new structure on manifolds: Silver structure, International Electronic Journal of Geometry, 9(2) (2016), 659-69.
  12. P. K. Pandey and Sameer, On the Adapted Connections on Kaehler-Norden Silver Manifolds, 26th International Conference of International Academy of Physical Sciences on Advances in Topology and Differential Geometry, Guru Ghasidas University, Bilaspur, India 2020.
  13. A. Primo and E. Reyes, Some algebraic and geometric properties of the Silver number, Mathematics and Informatics Quarterly, 18 (2007).
  14. A. Salimov and A. Gezer, Norden structures of Hessian type, Turk. J. Math., 38 (2014), 462-469. https://doi.org/10.3906/mat-1301-31
  15. A. Salimov, On anti-Hermitian metric connections, C. R. Math. Acad. Sci. Paris, 352 (9) (2014), 731-735. https://doi.org/10.1016/j.crma.2014.07.004
  16. B. Sahin and M. A. Akyol, Golden maps between Golden Riemannian manifolds and constancy of certain maps, Math. Commun., 19 (2014), 333-342.
  17. S. Tachibana, Analytic tensor and its generalization, Tohoku Math. J., 12 (2) (1960), 208-221. https://doi.org/10.2748/tmj/1178244436
  18. S. Turanli, A. Gezer, and H. Cakicioglu, Metallic Kahler and nearly metallic Kahler manifolds, Int. J. Geom. Methods Mod. Phys., (2021): 2150146.
  19. C. Udriste and G. Bercu, Riemannian Hessian metrics, Analele Univ. Bucur., 55 (2005), 189-204.
  20. K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics Vol. 3, World Scientific, Singapore, 1984.