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Year 2023, Volume: 6 Issue: 4, 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, Volume: 6 Issue: 4, 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 Volume: 6 Issue: 4

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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