Honam Mathematical Journal (호남수학학술지)

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OPERATORS ON METALLIC RIEMANNIAN STRUCTURES

  • Cayir, Hasim (Department of Mathematics, Giresun University)
  • Received : 2019.04.02
  • Accepted : 2019.05.20
  • Published : 2020.03.25
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Abstract

In this paper firstly, Some properties were given about metallic Riemannian structure on (1, 1)-tensor bundle. Secondly, the Tachibana and Vishnevskii operators were applied to vertical and horizontal lifts with respect to the metallic Riemannian structure on (1, 1)-tensor bundle, respectively.

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References

  1. M. A. Akyol and Y. Gunduzalp, Hemi-Slant Submersions from Almost Product Riemannian Manifolds, Gulf Journal of Mathematics, 4(3)(2016), 15-27.
  2. M. A. Akyol and Y. Gunduzalp, Hemi-Invariant Semi-Riemannian Submersions, Commun. Fac. Sci. Univ. Ank. Series A1, 67(1)(2018), 80-92.
  3. R. Cakan, On gh-lifts of Some Tensor Fields, Comptes rendus de l'Acade'mie bulgare des Sciences,71(3)(2018), 317-324.
  4. N. Cengiz and A. A. Salimov, Diagonal Lift in the Tensor Bundle and its Applications, Applied Mathematics and Computation, 142(2003) 309-319. https://doi.org/10.1016/S0096-3003(02)00305-3
  5. H. Cayir, Some Notes on Lifts of Almost Paracontact Structures, American Review of Mathematics and Statistics, 3(1)(2015), 52-60.
  6. H. Cayir, Tachibana and Vishnevskii Operators Applied to $X^V$ and $X^C$ in Almost Paracontact Structure on Tangent Bundle T(M), Ordu Universitesi Bilim ve Teknoloji Dergisi, 6(1) (2016), 67-82.
  7. H. Cayir, Tachibana and Vishnevskii Operators Applied to $X^V$ and $X^H$ in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences 4(3)(2016), 105-115. https://doi.org/10.20852/ntmsci.2016318821
  8. V.W. de Spinadel, The metallic means family and multifractal spectra. Nonlinear Anal Ser B, 36(1999), 721-745. https://doi.org/10.1016/S0362-546X(98)00123-0
  9. V.W. de Spinadel, The family of metallic means. Vis Math, 1(3) (1999).
  10. V.W. de Spinadel, The metallic means family and renormalization group techniques. Proc Steklov Inst Math Control Dynamic System, 1(2000), 194-209.
  11. V.W. de Spinadel, The metallic means family and forbidden symmetries. Int Math J., 2(2002), 279-288.
  12. A. Gezer, C . Karaman, On metallic Riemannian structures. Turk J Math 39(2015), 954-962. https://doi.org/10.3906/mat-1504-50
  13. S.I. Goldberg, K. Yano, Polynomial structures on manifolds. Kodai Math Sem Rep 22(1970), 199-218. https://doi.org/10.2996/kmj/1138846118
  14. C. Hretcanu, M. Cresmareanu, Metallic structures on Riemannian manifolds. Rev Un Mat Argentina 54(2013), 15-27.
  15. E. Musso and F. Tricerri, Riemannian Metric on Tangent Bundles, Ann. Math. Pura. Appl., 150(4)(1988), 1-9. https://doi.org/10.1007/BF01761461
  16. A. A. Salimov, On operators associted with tensor fields. J Geom, 99(2010), 107-145. https://doi.org/10.1007/s00022-010-0059-6
  17. A. A. Salimov, Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
  18. Y. Soylu, A Myers-type compactness theorem by the use of Bakry-Emery Ricci tensor, Differ. Geom. Appl., 54(2017), 245-250. https://doi.org/10.1016/j.difgeo.2017.04.005
  19. Y. Soylu, A compactness theorem in Riemannian manifolds, J. Geom., 109(20) 2018.
  20. A. A. Salimov and R. Cakan, Problem of g-lifts, Proceeding of the Institute of Mathematics and Mechanics, 43(1)(2017), 161-170.
  21. A. A. Salimov, H. Cayir, Some Notes On Almost Paracontact Structures, Comptes Rendus de 1'Acedemie Bulgare Des Sciences, 66(3)(2013), 331-338.
  22. A. A. Salimov, A. Gezer, On the geometry of the (1, 1)-tensor bundle with Sasaki type metric. Chinn Ann Math Ser B 32(2011), 369-386. https://doi.org/10.1007/s11401-011-0646-3
  23. B. Sahin, Semi-invariant Riemannian submersions from almost Hermitian manifolds, Canad.Math. Bull., 56(2013), 173-183. https://doi.org/10.4153/CMB-2011-144-8
  24. S. Tachibana, Analytic tensor and its generalization. Tohoku Math J 12(1968), 208-221. https://doi.org/10.2748/tmj/1178244436
  25. K. Yano, M. Ako, On certain operators associated with tensor fields. Kodai Math Sem Rep 20(1968), 414-436. https://doi.org/10.2996/kmj/1138845745