On Complete, Horizontal and Vertical Lifts From a Manifold With fλ(6,4) Structure to Its Cotangent Bundle

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Manisha M. Kankarej
Jai Pratap Singh

Abstract

Manifolds with fλ(6,4) structure was defined and studied in the past. Later the geometry of tangent and cotangent bundles in a differentiable manifold with fλ(6,4) structure was studied. The aim of the present paper is to study complete, horizontal and vertical lifts from a manifold with fλ(6,4)- structure to its cotangent bundle.

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References

  1. H. Cayir, Tachibana and Vishnevskii Operators Applied to XV and XH in Almost Paracontact Structure on Tangent Bundle T(M), New Trends Math. Sci. 4 (2016), 105-115. https://doi.org/10.20852/ntmsci.2016318821.
  2. H. Cayir, Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect To Xv and XH on Tangent Bundle T(M), Proc. Inst. Math. Mech. 42 (2016), 38-49.
  3. H. Cayir, Some Notes on Lifts of the ((ν+1), λ2(ν −1)) - Structure on Cotangent and Tangent Bundle, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70 (2021), 241–264. https://doi.org/10.31801/cfsuasmas.712861.
  4. L.S. Das, R. Nivas, V.N. Pathak, On Horizontal and Complete Lifts From a Manifold With fλ(7; 1)-Structure to Its Cotangent Bundle, Int. J. Math. Math. Sci. 8 (2005), 1291-1297. https://doi.org/10.1155/IJMMS.2005.1291.
  5. K.K. Dube, On a Differentiable Structure Satisfying f2v+4+f2=0; f6=0 of Type (1; 1), Nepali Math. Sci. Rep. 17 (1998), 99-102.
  6. J.B. Kim, Notes on f-Manifold, Tensor N-S, 29 (1975), 299-302.
  7. T. Li, D. Krupka, The Geometry of Tangent Bundles: Canonical Vector Fields, Geometry. 2013 (2013), 364301. https://doi.org/10.1155/2013/364301.
  8. 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 (2004), 35-41.
  9. S.K. Srivastava, R. Nivas, On Horizontal & Complete Lifts From a Manifold With fλ(7, −1) Structure to Its Cotangent Bundle, J. Tensor Soc. India, 14 (1996), 42-48.
  10. S.K. Srivastava, On the Complete Lifts of (1, 1) Tensor Field F Satisfying Structure Fν+1−λ2Fν−1=0, Nepali Math. Sci. Rep. 21 (2003), 89-99.
  11. M.D. Upadhyay, V.C. Gupta, Integrability Conditions of a F(K;−(K− 2)) - Structure Satisfying FK−FK−2=0; (F≠0; I), Rev. Univ. Nac. Tucuman, 20 (1976), 31-44.
  12. K. Yano, On a Structure Defined by a Tensor Field f of Type (1,1) Satisfying f3+f=0, Tensor N. S. 14 (1963), 99-109.
  13. K. Yano, C.S. Houh, B.Y. Chen, Structures Defined by a Tensor Field φ of Type (1,1) Satisfying φ4±φ2=0, Tensor N. S. 23 (1972), 81-87.
  14. K. Yano, S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, (1973).