Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

ON f-KENMOTSU MANIFOLDS ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

  • Received : 2021.01.17
  • Accepted : 2021.05.24
  • Published : 2021.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In the present paper, we study three-dimensional f-Kenmotsu manifolds admitting the Schouten-Van Kampen connection. We study the concircular curvature tensor of a three-dimensional f-Kenmotsu manifold with respect to the Schouten-Van Kampen connection. Finally, we have cited an example of a three-dimensional f-Kenmotsu manifold admitting Schouten-Van Kampen connection which verify our results.

Keywords

Acknowledgement

The author is thankful to the referee for his/her valuable comments and suggestions towards the improvement of the paper.

References

  1. E. Boeckx, P. Buecken and L. Vanhecke, φ-symmetric contact metric spaces, Glasgow Math. J. 52 (2005), 97-112.
  2. A. Bejancu, Schouten-van Kampen and Vranceanu connections on Foliated manifolds, Anale S,tintifice Ale Universitati."AL. I. CUZA' IASI, Tomul LII, Mathematica, 2006, 37-60.
  3. U. C. De and A. Sarkar, φ-Ricci symmetric Sasakian manifolds, Proceedings of the Janjeon Mathematical Society 11 (2008), 47-52.
  4. G. Ghosh, On Schouten-van Kampen connection in Sasakian manifolds, Boletim da Sociedade Paranaense de Mathematica 36 (2018), 171-182. https://doi.org/10.5269/bspm.v36i4.33105
  5. D. Janssens, and L. Vanheck, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), 1-27. https://doi.org/10.2996/kmj/1138036310
  6. W. Kuhnel, Conformal transformatons between Einstein spaces, Conformal geometry (Bonn, 1985/1986), 105-146, Aspects Math. E12, Friedr. Vieweg, Braunschweing, 1988.
  7. D. L. Kiran Kumar, H. G. Nagaraja and S. H. Naveenkumar, Some curvature properties of Kenmotsu manifolds with Schouten-van Kampen connection, Bull. of the Transilvania Univ. of Brasov., Series III: Math. Informatics, Phys. 2 (2019), 351-364.
  8. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku math. J. 24 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  9. A. Kazan and H. B. Karadag, Trans-Sasakian manifolds with Schouten-Van Kampen connection, Ilirias J. of Math. 7 (2018), 1-12.
  10. H. G. Nagaraja and D. L. Kiran Kumar, Kenmotsu manifolds admitting Schouten-van Kampen connection, Facta Univ. Series: Math. and Informations 34 (2019), 23-34.
  11. Z. Olszak, Locally conformal almost cosymplectic manifolds, Colloq. Math. 57 (1989), 73-87. https://doi.org/10.4064/cm-57-1-73-87
  12. Z. Olszak and R. Rosca, Normal locally conformal almost cosymplectice manifolds, Publ. Math. 39 (1991), 315-323.
  13. Z. Olszak, The Schouten-Van Kampen affine connection adapted to an almost(para) contact metric structure, Publications Delinstitut Mathematique 94 (2013), 31-42. https://doi.org/10.2298/PIM1308031O
  14. Y. S. Perktas and A. Yildiz, On f-Kenmotsu 3-manifolds with respect to the Schouten-van Kampen connection, Turkis J. of Math. 45 (2021), 387-409. https://doi.org/10.3906/mat-2003-121
  15. A. F. Solov'ev, On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geom. Sb. 19 (1978), 12-23 (in Russian).
  16. K. Yano, Concircular geometry I. concircular transformations, Proc. Inst. Acad. Tokyo 16 (1940), 195-200.
  17. K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Math. Studies 32, Princeton university press, 1953.
  18. A. Yildiz, U. C. De and M. Turan, On 3-dimensional f-Kenmotsu manifolds and Ricci soliton, Ukrainian J. Math. 65 (2013), 620-628.
  19. A. Yildiz, f-Kenmotsu manifolds with the Schouten-Van Kampen connection, Pub. De L'institut Math. 102 (116) (2017), 93-105. https://doi.org/10.2298/PIM1716093Y