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

Year 2023, , 170 - 175, 18.12.2023

Mohammad Nazrul Islam Khan Lovejoy Swapan Kumar Das

https://doi.org/10.32323/ujma.1359300

Cited By: 1

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.

Keywords

Riemannian manifold, Sasakian manifold, Tangent Bundle, Quartersymmetric semimetric connection

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.