LIFTING OF A GENERALISED ALMOST $r$-CONTACT STRUCTURE IN A TANGENT BUNDLE


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Authors

  • Mohit Saxena The Papua New Guinea University of Technology
  • Manisha M Kankarej Rochester Institue of Technology, Dubai, UAE
  • Riyaz Ahmad Khan Nizwa College of Technology, Sultanate of Oman https://orcid.org/0000-0002-2162-2621

Keywords:

Tangent bundle, complete lift, Lie derivative, horizontal lift, vertical lift

Abstract

Different structures defined on a differentiable manifold $M$ can be lifted to the same type of structures on its tangent bundle. Many researcher analysed herein obtained results in this vista. In this paper our aim is to study Lie derivatives in reference to the vertical and complete lifts of generalized almost r-contact structure in the tangent bundle. We investigate some theorems on induced Nijenhuis tensor in tangent bundle. Moreover, the complete lift of Hsu-structure along the cross section in tangent bundle is studied.

References

A. A. Salimov. Tensor operators and their applications, Nova Science Publ., New York,(2013).

A. Kazan, H. B. Karadog, Locally decomposable golden Riemannian tangent bundles with cheeger-gromoll metric,

Miskolc Mathematical Notes, 17(1) (2016), 399–411.

E. T. Davies. On the curvature of the tangent bundle. Annali di Mat. Pura ed Applicata, 81(1) (1969), 193–204.

F Ocak. Notes about tensor fields of type (1, 1) on the cross-section in the cotangent bundle. Transactions of NAS of

Azerbaijan, Issue Mathematics, Series of Physical-Technical and Mathematical Sciences, 36(4) (2016), 1–7.

J. Vanzura. Almost r-contact structure. Annali Della Scuola Normale, Superiore Di Pisa, 26(1) (1970), 97–115.

K. Yano and E. T. Davies. Metrics and connections in tangent bundle. Kodai Math. Sem. Rep., 23(4) (1971), 493–504.

K. Yano and S. Ishihara. Tangent and cotangent bundles. Marcel Dekker, Inc. New York, (1973).

K. Yano and S. Ishihara. Almost complex structures induced in tangent bundles. Kodai Math. Sem. Rep., 19 (1967),

–27.

L. S. Das, R. Nivas and M. N. I. Khan. On submanifolds of co-dimension 2 immersed in a Hsu-quaternion manifold.

Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 25(1) (2009), 129–135.

L. S. Das and M. N. I. Khan. Almost r -contact structures on the tangent bundle. Differential Geometry-Dynamical

Systems, 7 (2005), 34–41.

L. S. Das and R. Nivas. On certain structures defined on the tangent bundle. Rocky Mountain Journal of Mathematics,

(6) (2006), 1857–1866.

L. S. Das, R. Nivas and M. Saxena, A structure defined by a tensor field of type (1,1) satisfying (f 2 + a2

) (f 2 – a2

) (f 2 + b2

)

(f 2 – b2

) = 0, Tensor N. S., 65 (2004), 36–41.

M. N. I. Khan, Integrability of the Metallic Structures on the Frame Bundle, Kyungpook Mathematical Journal, 61(4)

(2021), 791–803.

M. N. I. Khan, M. A. Choudhary and S. K. Chaubey, Alternative Equations for Horizontal Lifts of the Metallic

Structures from Manifold onto Tangent Bundle, Journal of Mathematics, (2022), 5037620.

M. N. I. Khan, Submanifolds of a Riemannian manifold endowed with a new type of semi-symmetric non-metric connection in the tangent bundle, International Journal of Mathematics and Computer Science 17(1) (2022), 265–275.

M. N. I. Khan and Lovejoy S. Das, ON CR-structure and the general quadratic structure, Journal for Geometry and

Graphics, 24(2) (2020), 249–255.

M. N. I. Khan, Novel theorems for metallic structures on the frame bundle of the second order, Filomat 36(13) (2022),

–4482.

M. N. I. Khan, A note on certain structures in the tangent bundle, Far East Journal of Mathematical Sciences, 101(9)

(2017), 1947–1965.

M. N. I Khan, F Mofarreh and A Haseeb, Tangent Bundles of P-Sasakian Manifolds Endowed with a QuarterSymmetric Metric Connection, Symmetry, 15(3) (2023), 753.

M. N. I. Khan, F. Mofarreh, A. Haseeb and 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 (2024), 1553.

M. N. I. Khan, N. Fatima, A. Al Eid, B. B. Chaturvedi, M. Saxena, . Geometric Properties Of Submanifolds of a

Riemannian Manifold in Tangent Bundles, Results in Nonlinear Analysis, 7(2) (2024), 140–153.

M. N. I. Khan. Lifts of hypersurfaces with quarter-symmetric semi-metric connection to tangent bundles. Afrika

Matematika, Springer-Verlag, 25(2) (2014), 475–482.

M. N. I. Khan. Lift of semi-symmetric non-metric connection on a Kähler Manifold. Afrika Matematika SpringerVerlag, 27(3) (2016), 345–352.

M. N. I. Khan and De, U.C., Liftings of metallic structures to tangent bundles of order r, AIMS Mathematics, 7(5)

(2022), 7888–7897.

M. N. I. Khan, Lifts of hypersurfaces with quarter-symmetric semi-metric connection to tangent bundles, Afr. Mat.,

(2) (2014), 475–482.

M. N. I. Khan, Proposed theorems for lifts of the extended almost complex structures on the complex manifold, AsianEuropean Journal of Mathematics, 15(11) (2022), 2250200.

M. N. I. Khan, Tangent bundles endowed with semi-symmetric non-metric connection on a Riemannian manifold,

Facta Universitatis, Series: Mathematics and Informatics, 36(4) (2021), 855–878.

M. N.I. Khan, Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric

manifold, Chaos, Solitons & Fractals, 146 (2021), 110872.

M. N.I. Khan, U.C. De, and L.S. Velimirovic, Lifts of a quarter-symmetric metric connection from a Sasakian manifold

to its tangent bundle. Mathematics, 11(1) (2023), 53.

M. Saxena, Submersion on Statistical Metallic Manifold, Geometry of submanifolds and applications, In: Chen, BY.,

Choudhary, M.A., Khan, M.N.I. (eds), Publisher: Infosys Science Foundation Series in Mathematical Sciences, Springer,

Singapore, 1 (2024) 169–180, https://doi.org/10.1007/978-981-99-9750-31

M. Saxena, Lifts on the superstructure F(± a2

, ± b2

), obeying (F2 + a2

) (F2 – a2

) (F2 + b2

)(F2 – b2

) = 0, Journal of Science

and Art, 23(4) (2023) 965–972.

M. Saxena and P. K. Mathur, Decomposition of Special Pseudo Projective Curvature Tensor Field, Journal of Applied

Mathematics and Informatics, 41(5) (2023) 989–999.

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.

M. Tekkoyun. On lifts of paracomplex structures. Turk. J. Math., 30 (2006), 197–210.

R. Nivas and M. Saxena, On a special structure in a differentiable manifold, Demonstratio Mathematica, XXXIX(1)

(2006), 203–210.

R. Nivas and 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.

S. B. Mishra, M Saxena and P. K. Mathur, Aspects of invariant submanifold of a fλ Hsu manifold with compleented

frames, Journal of Rajasthan Academy Physical Sciences, 6(2) (2007), 179–188.

S. B. Mishra, P. K. Mathur and M Saxena, On APST Riemannian manifold with second order generalised structure,

Nepali Math. Sci. Rep, 27(1-2) (2007), 69–74.

S. Ianus and C. Udriste. On the tangent bundle of a differentiable manifold. Stud. Cercet. Mat., 22 (1970), 599–611.

T. Omran, A. Sharffuddin and S. I. Husain. Lift of structures on manifold. Publications De L’institut Mathematique

(Beograd) (N.S.), 36(50) (1984), 93–97

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Published

2024-08-16

How to Cite

Saxena, M. ., Kankarej, M. M., & Khan, R. A. (2024). LIFTING OF A GENERALISED ALMOST $r$-CONTACT STRUCTURE IN A TANGENT BUNDLE. Results in Nonlinear Analysis, 7(3), 194–201. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/464