Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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DECOMPOSITION OF SPECIAL PSEUDO PROJECTIVE CURVATURE TENSOR FIELD

  • Received : 2022.10.06
  • Accepted : 2023.05.15
  • Published : 2023.09.30
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Abstract

The aim of this paper is to study the projective curvature tensor field of the Curvature tensor Rijkh on a recurrent non Riemannian space admitting recurrent affine motion, which is also decomposable in the form Rijkh=Xi Yjkh, where Xi and Yjkh are non-null vector and tensor respectively. In this paper we decompose Special Pseudo Projective Curvature Tensor Field. In the sequal of decomposition we established several properties of such decomposed tensor fields. We have considered the curvature tensor field Rijkh in a Finsler space equipped with non symmetric connection and we study the decomposition of such field. In a special Pseudo recurrent Finsler Space, if the arbitrary tensor field 𝜓ij is assumed to be a covariant constant then, in view of the decomposition rule, 𝜙kh behaves as a recurrent tensor field. In the last, we have considered the decomposition of curvature tensor fields in Kaehlerian recurrent spaces and have obtained several related theorems.

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References

  1. L.A. Cordero, C.T. Dodson and M.D. Leon, Differential geometry of frame bundles, Springer Netherlands, Kluwer Academic Publishers, 1989.
  2. A. Kumar, On special pseudo projective projective recurrant tensor field, Acta Ciencia Indica. 3(1) (1970), 89-92.
  3. L.A. Cordero and M. De Leon, Prolongation of G-structures to the frame bundle, Ann. Mat. Pura. Appl. 143 (1986), 123-41. https://doi.org/10.1007/BF01769212
  4. H.D. Pande and H.S. Shukla, On the decomposition of the curvature tensor fields Kijkh and Hijkh in recurrent Finsler spaces, Indian. Pure Appl. Math. 8 (1977), 418-424.
  5. Ramhit, Decomposition of Berwald's curvature tensor fields, Ann. Fae. Sci.(Kinshasa) (1975), 220-226.
  6. O. Kowalski and M. Sekizawa, Curvatures of the diagonal lift from an affine manifold to the linear frame bundle, Cent. Eur. J. Math. 10 (2012), 37-43.
  7. L.S. Das, R. Nivas, M. Saxena, A structure defined by a tensor field of type (1, 1) satisfying (f2 + a2)(f2 - a2)(f2 + b2)(f2 - b2) = 0, Tensor N. S. 65 (2004), 36-41.
  8. B.B. Sinha and S.P. Singh, On decomposition of recurrent curvature tensor fields, Proe. Nat. Acad. Sci.(India) 40-A (1970), 105-110.
  9. R. Nivas, M. Saxena, On complete and horizontal lifts from a manifold with HSU-(4; 2) structure to its cotangent bundle, Nepali. Math. Sci. Rep. 23(2) (2004), 35-41.
  10. M.N.I. Khan, Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric manifold, Chaos, Solitons and Fractals 146 (2021), 110872.
  11. S. Gonul, I.K. Erken, A. Yazla, C. Murathan, A neutral relation between metallic structure and almost quadratic ϕ-structure, Turk. J. Math. 43 (2019), 268-78. https://doi.org/10.3906/mat-1807-72
  12. M. Ozkan and B. Peltek, A new structure on manifolds: Silver structure, Int. Electron. J. Geom. 9(2) (2016), 59-69. https://doi.org/10.36890/iejg.584592
  13. R. Nivas and M. Saxena, On a special structure in a differentiable manifold, Demonstratio Mathematica XXXIX (2006), 203-210. https://doi.org/10.1515/dema-2006-0124
  14. L. Bilen, S. Turanli and A. Gezer, On Kahler-Norden-Codazzi golden structures on pseudo-Riemannian manifolds, Int. J. Geom. Methods Mod. Phys. 15 (2018), 1-10. https://doi.org/10.1142/S0219887818500809
  15. C.E. Hretcanu and A.M. Blaga, Submanifolds in metallic Riemannian manifolds, Differ. Geometry-Dyn. Syst. 20 (2018), 83-97.
  16. M.N.I. Khan, Tangent bundle endowed with quarter-symmetric non-metric connection on an almost Hermitian manifold, Facta Univ. Ser. 35(1) (2020), 167-78. https://doi.org/10.22190/FUMI2001167K
  17. A. Sardar, M.N.I. Khan, U.C. De, n-Ricci Solitons and Almost co-Kahler Manifolds, Mathematics 9(24) 2100, 3200.
  18. S.B. Mishra, M. Saxena, P.K. Mathur, Aspects of invariant submanifold of a fλHsu manifold with compleented frames, Journal of Rajasthan Academy Physical Sciences 6 (2007), 179-188.
  19. S.B. Mishra, P.K. Mathur, M. Saxena, On APST Riemannian manifold with second order generalised structure, Nepali Math. Sci. Rep. 27 (2007), 69-74.
  20. M. Saxena, S. Ali and N. Goel, On the normal structure of a hypersurface in a -quasi sasakian manifold, Journal of The Tensor Society 14 (2020), 49-57. https://doi.org/10.56424/jts.v14i01.10606
  21. U.C. De, M.N.I. Khan, A. Sardar, h-Almost Ricci-Yamabe Solitons in Paracontact Geometry, Mathematics 10(18) (2022), 3388.
  22. M.N.I. Khan, U.C. De, Liftings of metallic structures to tangent bundles of order, AIMS Mathematics 7(5) (2022), 7888-7897. https://doi.org/10.3934/math.2022441