Investigations of a Riemannian manifold with a quarter symmetric metric (QSM) connection to its tangent bundle
Investigations of a Riemannian manifold with a QSM connection
Abstract views: 166
/ 
PDF downloads: 136
Keywords:
Connection, Gauss equation, Weingarten equation, Codazzi equation, Curvature tensor, Mathematical operators, Partial differential equations, Submanifold, Tangent bundleAbstract
The present paper aims to study a quarter symmetric metric connection in the
tangent bundle and investigate an induced metric and connection on a submanifold
of co-dimension 2 and hypersurface concerning the QSM connection in the tangent
bundle TM. Totally geodesic (TG) and totally umbilical (TU) concerning the QSM
connection on the submanifold of co-dimension 2 and hypersurface in TM are obtained.
References
O. Bahadir, Lorentzian para-Sasakian manifold with quarter-symmetric non-metric connection, Journal of Dynamical Systems and Geometricc Theories, 14 (2016), no. 1, 17-33.
L. S. Das, R. Nivas and M. N. I. Khan, On submanifolds of codimension 2 immersed in a hsu–quarternion manifold, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 25 (2009), no. 1, 129-135.
S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor, N. S.
(1975), 249-254.
H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34 (1932),
-50.
M. N. I. Khan, On generalized Ricci-Recurrent Lorentzian Para-Sasakian manifold,
Proceeding of National Academy of Sciences, 75(II), 147-148 (2005).
M. N. I. Khan and J. B. Jun, Lorentzian almost r-para-contact structure in the tangent
bundle, Journal of the Chungcheong Mathematical Society, 27(1), 29-34, 2014.
M. N. I. Khan, Novel theorems for the frame bundle endowed with metallic structures
on an almost contact metric manifold, Chaos, Solitons & Fractals, 146, may 2021,
D. H. Jin and J. W. Lee, Einstein half lightlike submanifolds of a Lorentzian space
form with a semi-symmetric metric connection, Quaestiones Mathematicae, 37, (2014),
no. 4, 485-505.
M. N. I. Khan, Lifts of hypersurfaces with quarter-symmetric semi-metric connection
to tangent bundles, Afrika Matematika, 27 (2014), 475-482.
M. N. I. Khan, F. Mofarreh and A. Haseeb, Tangent bundles of P-Sasakian manifolds
endowed with a QSM connection, Symmetry 15(3) (2023), 753.
M. N. I. Khan, F. Mofarreh, A. Haseeb and M. Saxena, Certain results on the lifts
from an LP-Sasakian manifold to its tangent bundle associated with a QSM connection,
Symmetry 15(8) (2023), 1553.
R. Kumar, L. Colney and M. N. I. Khan, Lifts of a semi-symmetric non-metric connection (SSNMC) from statistical manifolds to the tangent bundle, Results in Nonlinear
Analysis 6(3) (2023), 50–65.
M. N. I. Khan, Lifts of semi-symmetric non-metric connection on a K¨ahler manifold,
Afrika Matematika, 27 (2016), no. 3, 345-352.
M. N. I. Khan, Tangent bundle endowed with quarter-symmetric non-metric connection on an almost Hermitian manifold, Facta Universitatis, Series: Mathematics and
Informatics 35 (1), (2020) 167-178.
Suwais, K.; Ta¸s, N.; Ozg¨ur, N.; Mlaiki, N. Fixed Point Theorems ¨
in symmetric Controlled M-Metric type Spaces. Symmetry 2023, 15, 1665.
https://doi.org/10.3390/sym15091665.
Qaralleh, R.; Tallafha, A.; Shatanawi, W. Some Fixed-Point Results
in Extended S-Metric Space of type (α, β). Symmetry 2023, 15, 1790.
https://doi.org/10.3390/sym15091790.
M. M. Kankareja, S. Pandey and J. P. Singh, Fractional electromagnetic fields in DPS
and DNG regions with standard fractional vector cross product, Results in Nonlinear
Analysis 6 (2023) no.. 3, 76–81.
Y. Liang, On semi-symmetric recurrent-metric connection, Tensor N. S., 55(1994),
-112.
A. K. Mondal and U. C. De, Some properties of a QSM connection on a sasakian
manifold, Bulletin of Mathematical analysis and applications, 1 (2009), no. 2, 99-108.
S. Mukhopadhyay, A. K. Roy and B. Barua, Some properties of a QSM connection
on a Riemannian manifold, Soochow J. of Math. 17 (1991), no. 2, 205-211.
M. Ozkan and F. Yılmaz, Prolongations of Golden Structures to Tangent Bundles of ¨
Order, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 65 (1) (2016), 35-47.
R. Prasad and A. Haseeb, Conformal curvature tensor on K-contact manifold with
respect to the QSM connection, FACTA UNIVERSITATIS (NIS) Ser. Math. Inform,
(2017), no. 4, 503-514.
E. Pak, On the pseudo-Riemannian spaces, J. Korean Math. Soc. 6 (1969), 23-31.
Rahim, M.; Shah, K.; Abdeljawad, T.; Aphane, M.; Alburaikan, A.; Khalifa, H.
A. E. W. Confidence Levels-Based p, q-Quasirung Orthopair Fuzzy Operators and
Its Applications to Criteria Group Decision Making Problems, IEEE Access 2023, 1,
-109996. 10.1109/ACCESS.2023.3321876
S. Sular, C. Ozgur and U. C. De, Quarter symmetric metric connection in a Kenmotsu
manifold, SUT Journal of mathematics 44 (2008), no. 2, 297-306.
M. Tani, Prolongations of hypersurfaces of tangent bundles, Kodai Math. Semp. Rep 21 (1969), 85-96.
S. Ali and R. Nivas, On submanifolds immersed in a manifold with quarter-symmetric connection, Riv. Mat. Univ. Parma. 6 (3) (2000), 11-23.
K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, 1973.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.
