Mohammad Nazrul Islam Khan, O\u{g}uzhan Bahad\i r

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The aim of the present work is to study and establish conditions for an
LP-Sasakian manifold on the tangent bundle $TM$. An LP-Sasakian manifold with the generalized symmetric metric connection on $TM$ is investigated. Next, the curvature tensor and the Ricci tensor of an LP-Sasakian manifold with respect to the generalized symmetric metric connection on $TM$ are calculated. Moreover, the projective curvature tensor with respect to the generalized symmetric metric connection on $TM$ is studied and showed that $TM$ is not $\hat{\xi}^C$-projectively flat. In particular, if $\alpha=0$ and $\beta=1$ then $TM$ is $\hat{\xi}^C$-projectively flat.


LP-Sasakian manifold, Tangent bundle, Mathematical operators, Curva- ture tensor, Ricci tensor, Projective curvature tensor, Partial differential equations

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bibitem{NM} {sc N. S. Agashe {rm and} M. R. Chafle}: textit{A semi symetric non-metric connection in a Riemannian manifold}. Indian J. Pure Appl. Math.{bf 23} (1992), 399--409.


bibitem{OB} {sc O. Bahadir}: textit{ Lorentzian para-Sasakian manifold with quartersymmetric non-metric connection}. Journal of Dynamical Systems and Geometric Theories {bf 14}(1) (2016), 17--33.


bibitem{LM} {sc L. S. Das {rm and} M. N. I. Khan}: textit{Almost r-contact structure in the tangent bundle}. Differential Geometry-Dynamical System {bf7} (2005), 34--41.

bibitem{DKS} {sc L. S. Das {rm and} M. N. I. Khan}: textit{Symmetric and Ricci LP-Sasakian manifold}. Mathematical Sciences Research Journal {bf17}(10) (2013), 263--268.


bibitem{UD} {sc U. C. De {rm and} D. Kamilya}: textit{Hypersurfaces of Rieamnnian manifold with semi-symmetric non-metric connection}. J. Indian Inst. Sci. {bf75} (1995), 707--710.


bibitem{AJ} {sc A. Friedmann {rm and} J. A. Schouten}: textit{"{A}Uber diegeometrie der halbsymmetrischen "{A}ubertragung}. Math. Zeitschr. {bf21} (1924), 211--223.


bibitem{SG} {sc S. Golab}: textit{On semi-symmetric and quarter-symmetric linear connections}. Tensor N. S. {bf29} (1975), 249--254.

bibitem{HA} {sc H. A. Hayden}: textit{ Subspaces of a space with torsion}. Proc. London Math. Soc. {bf 34} (1932), 27--50.


bibitem{SSCA} {sc S. K. Hui, S. Uddin, C. Ozel {rm and} A. A. Mustafa}: textit{ Warped product submanifolds of LP-Sasakian manifolds}: Hindawi Publishing Corporation, Discrete Dynamics in Nature and Society, {bf2012}, Article ID 868549, 11 pages.


bibitem{MJ} {sc M. N. I. Khan {rm and} J. B. Jun}: textit{Lorentzian almost r-para-contact structure in tangent bundle}. Journal of the Chungcheong Mathematical Society {bf 27}(1) (2014), 29--34.


bibitem{KQ} {sc M. N. I. Khan}: textit{Quarter-symmetric semi-metric connection on a Sasakian manifold}. Tensor N.S., {bf 68}(2) (2007), 154--157.


bibitem{MNC}{sc M. N. I. Khan}: textit{Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric manifold}. Chaos, Solitons & Fractals. {bf 146}, May 2021, 110872.


bibitem{MK} {sc M. N. I. Khan}: textit{ Tangent bundle endowed with quarter-symmetric non-metric connection on an almost Hermitian manifold}. Facta Universitis (NIS) Ser. Math. Inform. {bf 35}(1) (2020), 167--178.


bibitem{MNI} {sc M. N. I. Khan}: textit{ Lifts of hypersurfaces with quarter-symmetric semi-metric connection to tangent bundles}. Afrika Matematika textbf{25} (2014), 475--482.


bibitem{MNIK} {sc M. N. I. Khan}:textit{ Lifts of semi-symmetric non-metric connection on a Kahler manifold}. Afrika Matematika {bf 27}(3) (2016), 345--352.


bibitem{YL} {sc Y. Liang}: textit{On semi-symmetric recurrent-metric connection}. Tensor {bf55} (1994), 107--112.


bibitem{KM} {sc K. Matsumoto}: textit{On Lorentzian Paracontact manifolds}. Bull. Yamagata Univ. Natur. Sci. {bf12}(2) (1989), 151--156.


bibitem{IR} {sc I. Mihai {rm and} R. Rosca}: textit{On Lorentzian P-Sasakian manifolds, Clssical Analysis}. World Scientific Publ., Signapore, (1992), 155--169.


bibitem{KI}{sc K. Matsumoto {rm and} I. Mihai}: textit{On a certain transformation in a Lorentzian para Sasakian manifold}. Tensor N. S. {bf47} (1988), 189--197.


bibitem{IAU} {sc I. Mihai, A. A. Shaikh {rm and} U. C. De}: textit{On Lorentzian para-Sasakian manifolds}. Rendiconti del Seminario Mat. di Messina, Serie II 1999.


bibitem{AU} {sc A. K. Mondal {rm and} U. C. De}: textit{Some properties of a quarter-symmetric metric connection on a sasakian manifold}. Bulletin of Mathematical analysis and applications, {bf3}(1) (2009), 99--108.


bibitem{AUQ} {sc A. K. Mondal {rm and} U. C. De}: textit{Quarter-symmetric Nonmetric Connection on P-sasakian manifolds}. ISRN Geometry, {bf 2012}, Article ID 659430, 14 pages.


bibitem{SES} {sc S. Y. Perktas, E. Kilic {rm and} S. Keles}: textit{On a semi-symmetric non-metric connection in an LP-Sasakian manifold}. Int. Electron. J. Geom. {bf 3}(2), (2010), 15--25.


bibitem{SR} {sc S. K. Srivastava {rm and} R. P. Kushwaha}: textit{Lorentzian para Sasakian manifolds admitting special semi-symmetric recurrent metric connection}. Global Journal of Science Frontier Research Mathematics and Decision Sciences {bf 13}(7) Version 1.0 (2013), 1--7.


bibitem{SS} {sc S. Sharfuddin {rm and} S. I. Husain}:textit{Semi-symmetric metric connexions in almost contact manifolds}. Tensor N. S. {bf30} (1976), 133--139.


bibitem{BG} {sc B. G. Schmidt}: textit{Conditions on a connection to be a metric connection}. Commun. Math. Phys. {bf29} (1973), 55--59.


bibitem{MT} {sc M. Tani}: textit{Prolongations of hypersurfaces of tangent bundles}. Kodai Math. Semp. Rep. {bf 21} (1969), 85--96.

DOI: https://doi.org/10.22190/FUMI221026009K


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