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Article

Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle

by
Mohammad Nazrul Islam Khan
1,*,
Uday Chand De
2 and
Ljubica S. Velimirović
3
1
Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia
2
Department of Pure Mathematics, University of Calcutta 35, Ballygaunge Circular Road, Kolkata 700019, India
3
Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, 18 000 Niš, Serbia
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(1), 53; https://doi.org/10.3390/math11010053
Submission received: 29 November 2022 / Revised: 16 December 2022 / Accepted: 19 December 2022 / Published: 23 December 2022
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
Versions Notes

Abstract

The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle was established. Some theorems on the curvature tensor and the projective curvature tensor of a Sasakian manifold with respect to the quarter-symmetric metric connection to its tangent bundle were proved. Finally, locally ϕ-symmetric Sasakian manifolds with respect to the quarter-symmetric metric connection to its tangent bundle were studied.
Keywords: complete lift; tangent bundle; quarter-symmetric metric connection; Sasakian manifold; curvature tensor; projective curvature tensor; locally ϕ-symmetric complete lift; tangent bundle; quarter-symmetric metric connection; Sasakian manifold; curvature tensor; projective curvature tensor; locally ϕ-symmetric

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MDPI and ACS Style

Khan, M.N.I.; De, U.C.; Velimirović, L.S. Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle. Mathematics 2023, 11, 53. https://doi.org/10.3390/math11010053

AMA Style

Khan MNI, De UC, Velimirović LS. Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle. Mathematics. 2023; 11(1):53. https://doi.org/10.3390/math11010053

Chicago/Turabian Style

Khan, Mohammad Nazrul Islam, Uday Chand De, and Ljubica S. Velimirović. 2023. "Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle" Mathematics 11, no. 1: 53. https://doi.org/10.3390/math11010053

APA Style

Khan, M. N. I., De, U. C., & Velimirović, L. S. (2023). Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle. Mathematics, 11(1), 53. https://doi.org/10.3390/math11010053

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