Research Article
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Year 2023, , 170 - 175, 18.12.2023
https://doi.org/10.32323/ujma.1359300

Abstract

References

  • [1] S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N. S.), 29 (1975), 249.
  • [2] R. S. Mishra, S. N. Pandey, On quarter symmetric metric F-connection, Tensor (N. S.), 34 (1980), 1-7.
  • [3] M. N. I. Khan, S. Lovejoy, On CR-structure and the general quadratic structure, J. Geom. Graph., 24(2) (2020), 249-255.
  • [4] H.M. Dida, F. Hathout, Ricci soliton on the tangent bundle with semi-symmetric metric connection, Bull. Transilv. Univ. Bras. Ser. III Math. Comput. Sci., 1 (2021), 37–52.
  • [5] H.M. Dida, A. Ikemakhen, A class of metrics on tangent bundles of pseudo-Riemannian manifolds, Arch. Math. (BRNO) Tomus, 47 (2011), 293–308.
  • [6] E. Peyghan, F. Firuzi, U. C. De, Golden Riemannian structures on the tangent bundle with g-natural metrics, Filomat, 33 (2019), 2543–2554.
  • [7] M. Altunbas, Ricci solitons on tangent bundles with the complete lift of a projective semi-symmetric connection, Gulf J. Math., 14 (2023), 8–15.
  • [8] 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(8) (2023), 1553.
  • [9] M. Tani, Prolongations of hypersurfaces of tangent bundles, Kodai Math. Semp. Rep., 21 (1969), 85.
  • [10] 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. Comput. Sci., 17(1) (2022), 265–275. [11] B. Barua, S. Mukhopadhayay, A sequence of semimetric connection on a Riemannian manifold, Proceeding of Seventh National Seminar on Finsler-Lagrange and Hamilton Spaces, Brasov, Romania, 1992.
  • [12] M. N. I. Khan, Novel theorems for metallic structures on the frame bundle of the second order, Filomat, 36(13) (2022), 4471–4482.
  • [13] H. A. Hayden, Subspace of a space with torsion, Proceeding of the London Math. Society II Series 34, 27, 1932.
  • [14] K. Yano, On semi-symmetric connections, Rev. Roum. Math. Pures et Appl., 15 (1970), 1579.
  • [15] M.N.I. Khan, Liftings from a para-Sasakian manifold to its tangent bundles, Filomat, 37(20) (2023), 6727-6740.
  • [16] M. A. Choudhary, M. N. I. Khan, M. D. Siddiqi, Some basic inequalities on (e)-para Sasakian manifold, Symmetry, 14(12) (2022), 2585.
  • [17] T. Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor (N.S.), 23, (1972), 300.
  • [18] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Sringer-Verlog, Berlim, 1976.
  • [19] R. Kumar, L. Colney, M. N. I. Khan, Proposed theorems on the lifts of Kenmotsu manifolds admitting a non-symmetric non-metric connection (NSNMC) in the tangent bundle, Symmetry, 15(11), 2037.
  • [20] S. Sasaki, Lectures Notes on Almost Contact Manifolds, Part I, Tohoku University, 1965.
  • [21] H. I. Yoldas, S. E. Meric¸, E. Yasar, On generic submanifold of Sasakian manifold with concurrent vector field, Commun. Fac. of Sci. Univ. Ank. Ser. A1 Math. Stat. 68(2) (2019), 1983-1994.
  • [22] K. Yano, S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, 1973.
  • [23] K. De, M. N. I. Khan, U. C. De, Almost co-K¨ahler manifolds and quasi-Einstein solitons, Chaos, Solitons Fractals, 167 (2023), 113050.
  • [24] H. I. Yoldas, A. Haseeb, F. Mofarreh, Certain curvature conditions on Kenmotsu manifolds and 􀀀h0-Ricci solitons, Axioms, 12(2) (2023), 140.
  • [25] M.N.I. Khan, F. Mofarreh, A Haseeb, Tangent bundles of P-Sasakian manifolds endowed with a quarter-symmetric metric connection, Symmetry, 15(3) (2023), 753.
  • [26] M. N. I. Khan, U. C. De, Lifts of metallic structure on a cross-section, Filomat, 36(18), (2022), 6369-6363.
  • [27] A. Friedmann, J. A. Schouten, Uber die geometric der halbsymmetricschen ubertragungen, Math Z., 21 (1924), 211.
  • [28] A. C. Gozutk, E. Esin, Tangent bundle of hypersurface with a semi-symmetric metric connection, Int. J. Contemp. Math. Sciences, 7(6) (2012), 279.
  • [29] L. S. Das, R. Nivas, M. N. I. Khan, On semi-invariant submanifolds of conformal K(x ) contact Riemannian manifold, Algebras Groups Geom., 23(1) (2006), 292-302.

Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle

Year 2023, , 170 - 175, 18.12.2023
https://doi.org/10.32323/ujma.1359300

Abstract

The aim of the present paper is to introduce a Sasakian manifold immersed with a quartersymmetric semimetric connection to a tangent bundle. Some basic results are given on a Riemannian connection and a QSSC to the tangent bundle on a Sasakian manifold. The geometrical properties of a Sasakian manifold to its tangent bundle are also discussed.

References

  • [1] S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N. S.), 29 (1975), 249.
  • [2] R. S. Mishra, S. N. Pandey, On quarter symmetric metric F-connection, Tensor (N. S.), 34 (1980), 1-7.
  • [3] M. N. I. Khan, S. Lovejoy, On CR-structure and the general quadratic structure, J. Geom. Graph., 24(2) (2020), 249-255.
  • [4] H.M. Dida, F. Hathout, Ricci soliton on the tangent bundle with semi-symmetric metric connection, Bull. Transilv. Univ. Bras. Ser. III Math. Comput. Sci., 1 (2021), 37–52.
  • [5] H.M. Dida, A. Ikemakhen, A class of metrics on tangent bundles of pseudo-Riemannian manifolds, Arch. Math. (BRNO) Tomus, 47 (2011), 293–308.
  • [6] E. Peyghan, F. Firuzi, U. C. De, Golden Riemannian structures on the tangent bundle with g-natural metrics, Filomat, 33 (2019), 2543–2554.
  • [7] M. Altunbas, Ricci solitons on tangent bundles with the complete lift of a projective semi-symmetric connection, Gulf J. Math., 14 (2023), 8–15.
  • [8] 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(8) (2023), 1553.
  • [9] M. Tani, Prolongations of hypersurfaces of tangent bundles, Kodai Math. Semp. Rep., 21 (1969), 85.
  • [10] 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. Comput. Sci., 17(1) (2022), 265–275. [11] B. Barua, S. Mukhopadhayay, A sequence of semimetric connection on a Riemannian manifold, Proceeding of Seventh National Seminar on Finsler-Lagrange and Hamilton Spaces, Brasov, Romania, 1992.
  • [12] M. N. I. Khan, Novel theorems for metallic structures on the frame bundle of the second order, Filomat, 36(13) (2022), 4471–4482.
  • [13] H. A. Hayden, Subspace of a space with torsion, Proceeding of the London Math. Society II Series 34, 27, 1932.
  • [14] K. Yano, On semi-symmetric connections, Rev. Roum. Math. Pures et Appl., 15 (1970), 1579.
  • [15] M.N.I. Khan, Liftings from a para-Sasakian manifold to its tangent bundles, Filomat, 37(20) (2023), 6727-6740.
  • [16] M. A. Choudhary, M. N. I. Khan, M. D. Siddiqi, Some basic inequalities on (e)-para Sasakian manifold, Symmetry, 14(12) (2022), 2585.
  • [17] T. Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor (N.S.), 23, (1972), 300.
  • [18] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Sringer-Verlog, Berlim, 1976.
  • [19] R. Kumar, L. Colney, M. N. I. Khan, Proposed theorems on the lifts of Kenmotsu manifolds admitting a non-symmetric non-metric connection (NSNMC) in the tangent bundle, Symmetry, 15(11), 2037.
  • [20] S. Sasaki, Lectures Notes on Almost Contact Manifolds, Part I, Tohoku University, 1965.
  • [21] H. I. Yoldas, S. E. Meric¸, E. Yasar, On generic submanifold of Sasakian manifold with concurrent vector field, Commun. Fac. of Sci. Univ. Ank. Ser. A1 Math. Stat. 68(2) (2019), 1983-1994.
  • [22] K. Yano, S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, 1973.
  • [23] K. De, M. N. I. Khan, U. C. De, Almost co-K¨ahler manifolds and quasi-Einstein solitons, Chaos, Solitons Fractals, 167 (2023), 113050.
  • [24] H. I. Yoldas, A. Haseeb, F. Mofarreh, Certain curvature conditions on Kenmotsu manifolds and 􀀀h0-Ricci solitons, Axioms, 12(2) (2023), 140.
  • [25] M.N.I. Khan, F. Mofarreh, A Haseeb, Tangent bundles of P-Sasakian manifolds endowed with a quarter-symmetric metric connection, Symmetry, 15(3) (2023), 753.
  • [26] M. N. I. Khan, U. C. De, Lifts of metallic structure on a cross-section, Filomat, 36(18), (2022), 6369-6363.
  • [27] A. Friedmann, J. A. Schouten, Uber die geometric der halbsymmetricschen ubertragungen, Math Z., 21 (1924), 211.
  • [28] A. C. Gozutk, E. Esin, Tangent bundle of hypersurface with a semi-symmetric metric connection, Int. J. Contemp. Math. Sciences, 7(6) (2012), 279.
  • [29] L. S. Das, R. Nivas, M. N. I. Khan, On semi-invariant submanifolds of conformal K(x ) contact Riemannian manifold, Algebras Groups Geom., 23(1) (2006), 292-302.
There are 28 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Articles
Authors

Mohammad Nazrul Islam Khan 0000-0002-9652-0355

Lovejoy Swapan Kumar Das 0000-0002-2709-5113

Early Pub Date December 15, 2023
Publication Date December 18, 2023
Submission Date September 12, 2023
Acceptance Date December 8, 2023
Published in Issue Year 2023

Cite

APA Khan, M. N. I., & Das, L. S. K. (2023). Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle. Universal Journal of Mathematics and Applications, 6(4), 170-175. https://doi.org/10.32323/ujma.1359300
AMA Khan MNI, Das LSK. Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle. Univ. J. Math. Appl. December 2023;6(4):170-175. doi:10.32323/ujma.1359300
Chicago Khan, Mohammad Nazrul Islam, and Lovejoy Swapan Kumar Das. “Lifts of Hypersurfaces on a Sasakian Manifold With a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle”. Universal Journal of Mathematics and Applications 6, no. 4 (December 2023): 170-75. https://doi.org/10.32323/ujma.1359300.
EndNote Khan MNI, Das LSK (December 1, 2023) Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle. Universal Journal of Mathematics and Applications 6 4 170–175.
IEEE M. N. I. Khan and L. S. K. Das, “Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle”, Univ. J. Math. Appl., vol. 6, no. 4, pp. 170–175, 2023, doi: 10.32323/ujma.1359300.
ISNAD Khan, Mohammad Nazrul Islam - Das, Lovejoy Swapan Kumar. “Lifts of Hypersurfaces on a Sasakian Manifold With a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle”. Universal Journal of Mathematics and Applications 6/4 (December 2023), 170-175. https://doi.org/10.32323/ujma.1359300.
JAMA Khan MNI, Das LSK. Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle. Univ. J. Math. Appl. 2023;6:170–175.
MLA Khan, Mohammad Nazrul Islam and Lovejoy Swapan Kumar Das. “Lifts of Hypersurfaces on a Sasakian Manifold With a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle”. Universal Journal of Mathematics and Applications, vol. 6, no. 4, 2023, pp. 170-5, doi:10.32323/ujma.1359300.
Vancouver Khan MNI, Das LSK. Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle. Univ. J. Math. Appl. 2023;6(4):170-5.

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