Lifts of Almost Product Structures From Manifolds to Tangent Bundles

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DOI: https://doi.org/10.28924/2291-8639-22-2024-116
Published: Jul 19, 2024
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Manisha M. Kankarej, Lifts of Almost Product Structures From Manifolds to Tangent Bundles, Int. J. Anal. Appl., 22 (2024), 116.

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Manisha M. Kankarej

Abstract

In the present paper I have explored the properties of complete and horizontal lifts of an almost product structure. Its partial integrability and integrability conditions on the tangent bundle are part of this study. Along with different theorems on the lifts the prolongation of an almost product structure on the third tangent bundle T3M has been explored.

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References

  1. M. Altunbas, L. Bilen, A. Gezer, Remarks About the Kaluza-Klein Metric on Tangent Bundle, Int. J. Geom. Methods Mod. Phys. 16 (2019), 1950040. https://doi.org/10.1142/s0219887819500403.
  2. S. Azami, General Natural Metallic Structure on Tangent Bundle, Iran. J. Sci. Technol. Trans. Sci. 42 (2018), 81–88. https://doi.org/10.1007/s40995-018-0488-x.
  3. M.N.I. Khan, U.C. De, T. Alam, Characterizations of the Frame Bundle Admitting Metallic Structures on Almost Quadratic φ-Manifolds, Mathematics 11 (2023), 3097. https://doi.org/10.3390/math11143097.
  4. H.M. Dida, F. Hathout, Ricci Soliton on the Tangent Bundle With Semi-Symmetric Metric Connection, Bull. Transilv. Univ. Bras, ov Ser. III Math. Comput. Sci. 1 (2022), 37–52. https://doi.org/10.31926/but.mif.2021.1.63.2.4.
  5. H.M. Dida, A. Ikemakhen, A Class of Metrics on Tangent Bundles of Pseudo-Riemannian Manifolds, Arch. Math. 47 (2011), 293–308. https://eudml.org/doc/247005.
  6. H.M. Dida, F. Hathout, M. Djaa, On the Geometry of the Second Order Tangent Bundle With the Diagonal Lift Metric, Int. J. Math. Anal. 3 (2009), 443–456.
  7. S.I. Goldberg, K. Yano, Polynomial Structures on Manifolds, Kodai Math. J. 22 (1970), 199–218. https://doi.org/10.2996/kmj/1138846118.
  8. S.I. Goldberg, N.C. Petridis, Differentiable Solutions of Algebraic Equations on Manifolds, Kodai Math. J. 25 (1973), 111–128. https://doi.org/10.2996/kmj/1138846727.
  9. M.M. Kankarej, J.P. Singh, On Complete, Horizontal and Vertical Lifts From a Manifold With fλ(6, 4) Structure to Its Cotangent Bundle, Int. J. Anal. Appl. 20 (2022), 56. https://doi.org/10.28924/2291-8639-20-2022-56.
  10. M.N.I. Khan, F. Mofarreh, A. Haseeb, M. Saxena, Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection, Symmetry 15 (2023), 1553. https://doi.org/10.3390/sym15081553.
  11. M.N.I. Khan, U.C. De, Liftings of Metallic Structures to Tangent Bundles of Orderr, AIMS Math. 7 (2022), 7888–7897. https://doi.org/10.3934/math.2022441.
  12. M.N.I. Khan, U.C. De, L.S. Velimirovi´c, Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle, Mathematics 11 (2022), 53. https://doi.org/10.3390/math11010053.
  13. M. N. I. Khan, Lifts of F(α, β)(3, 2, 1) structures from manifolds to tangent bundles, Facta Univ. Ser. Math. Inf. 38 (2023), 209–218.
  14. M.N.I. Khan, Submanifolds of a Riemannian Manifold Endowed With a New Type of Semi-Symmetric Non-Metric Connection in the Tangent Bundle, Int. J. Math. Comp. Sci. 17 (2022), 265–275.
  15. M.N.I. Khan, Proposed Theorems for Lifts of the Extended Almost Complex Structures on the Complex Manifold, Asian-Eur. J. Math. 15 (2022), 2250200. https://doi.org/10.1142/s179355712250200x.
  16. M.N.I. Khan, Integrability of the Metallic Structures on the Frame Bundle, Kyungpook Math. J. 61 (2021), 791–803. https://doi.org/10.5666/KMJ.2021.61.4.791.
  17. M.N.I. Khan, U.C. De, Lifts of Metallic Structure on a Cross-Section, Filomat 36 (2022), 6369–6373. https://doi.org/10.2298/fil2218369k.
  18. T. Omran, A. Sharffuddin, S.I. Husain, Lift of Structures on Manifold, Publ. Inst. Math. (N.S.), 36 (1984), 93–97.
  19. E. Peyghan, F. Firuzi, U.c. De, Golden Riemannian Structures on the Tangent Bundle With g-Natural Metrics, Filomat 33 (2019), 2543–2554. https://doi.org/10.2298/fil1908543p.
  20. M. Tekkoyun, On Lifts of Para Complex Structures, Turk. J. Math. 30 (2006), 197–210.
  21. K. Yano, S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, 1973.
  22. K. Yano, S. Ishihara, Almost Complex Structures Induced in Tangent Bundles, Kodai Math. Sem. Rep. 19 (1967), 1–27. https://doi.org/10.2996/kmj/1138845336.