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η-Ricci Solitons in δ-Lorentzian Trans Sasakian Manifolds with a Semi-symmetric Metric Connection
Siddiqi, Mohd Danish Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.3
The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.
η-Einstein Solitons on (ε)-Kenmotsu Manifolds
MOHD. DANISH SIDDIQI,Sudhakar Kumar Chaubey 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.4
The objective of this study is to investigate η-Einstein solitons on (ε)-Kenmotsu manifolds when the Weyl-conformal curvature tensor satisfies some geometric properties such as being flat, semi-symmetric and Einstein semi-symmetric. Here, we discuss the properties of η-Einstein solitons on φ-symmetric (ε)-Kenmotsu manifolds.
Ƞ-RICCI SOLITONS ON TRANS-SASAKIAN MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION
( Oğuzhan Bahadir ),( Mohd Danish Siddiqi ),( Mehmet Akif Akyol ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its cur- vature tensor and Ricci tensor are calculated. Also, we study the Ƞ-Ricci solitons on a Trans-Sasakian Manifolds with quarter- symmetric non-metric connection. Indeed, we investigated that the Ricci and Ƞ-Ricci solitons with quarter-symmetric non-metric con- nection satisfying the conditions □.□ = 0. In a particular case, when the potential vector field ξ of the Ƞ-Ricci soliton is of gradi- ent type ξ = grad(ψ), we derive, from the Ƞ-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an exam- ple for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the Ƞ-Ricci solitons.
Mobin Ahmad,전재복,MOHD. DANISH SIDDIQI 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
In this paper a semi-symmetric non-metric connection in a nearly trans-Sasakian manifold is defined and semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a semi-symmetric non-metric connection is studied. Moreover, Nijenhuis tensor is calculated and integrability conditions of the distributions on semi-invariant submanifolds are discussed.
ALMOST QUASI-YAMABE SOLITONS ON LORENTZIAN CONCIRCULAR STRUCTURE MANIFOLDS-[(LCS)<sub>n</sub>]
( Jae-bok Jun ),( Mohd. Danish Siddiqi ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
The object of the present paper is to study of Almost Quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons on an Lorentzian concircular structure manifolds briey say (LCS)<sub>n</sub>-manifolds under infinitesimal CL-transformations and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Also we obtained a necessary and sufficient condition of an almost quasi-Yamabe soliton with respect to the CL-connection to be an almost quasi-Yamabe soliton on (LCS)<sub>n</sub>-manifolds with respect to Levi-Civita connection. Finally, we construct an example of steady almost quasi-Yamabe soliton on 3-dimensional (LCS)<sub>n</sub>-manifolds.
Semi-symmetric semi-metric connection in a Lorentzian β-Kenmotsu manifold
Abdul Haseeb,전재복,MOHD. DANISH SIDDIQI,Mobin Ahmad 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.4
In the present paper, we consider a semi-symmetric semi-metric connection in a Lorentzian β-Kenmotsu manifold. We investigate the curvature tensor and the Ricci tensor of a Lorentzian β-Kenmotsu manifold with a semi-symmetric semi-metric connection. Moreover, we consider pseudo projectively flat, ξ-pseudo projectively flat and Φ-pseudo projectively semisymmetric Lorentzian β-Kenmotsu manifolds with a semi-symmetric semi-metric connection and obtain the scalar curvature r in each case.
Mobin Ahmad,Jae-Bok Jun,Mohd Danish Siddiqi 충청수학회 2012 충청수학회지 Vol.25 No.1
We de¯ne a quarter-symmetric non-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a quarter-symmetric non-metric connection. Moreover, we also ob-tain integrability conditions of the distributions on semi-invariant submanifolds.