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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.
Quasi-concircular curvature tensor on a Lorentzian $\beta$-Kenmotsu manifold
Mobin Ahmad,Abdul Haseeb,전재복 충청수학회 2019 충청수학회지 Vol.32 No.3
In the present paper, we study quasi-concircular curvature tensor satisfying certain curvature conditions on a Lorentzian $\beta$-Kenmotsu manifold with respect to the semi-symmetric semi-metric connection.
Mobin Ahmad,Jae-Bok Jun,Abdul Haseeb 충청수학회 2011 충청수학회지 Vol.24 No.1
We dene a quarter-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider the submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection. We also obtain the Gauss, Codazzi and Weingarten equations and the cur- vature tensor for the submanifolds of an almost r-paracontact Rie- mannian manifold endowed with a quarter-symmetric non-metric connection.
Mobin Ahmad,전재복,Abdul Haseeb 대한수학회 2009 대한수학회보 Vol.46 No.3
We define a quarter symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider invariant,non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection.
QUASI-CONCIRCULAR CURVATURE TENSOR ON A LORENTZIAN β-KENMOTSU MANIFOLD
Mobin Ahmad,Abdul Haseeb,Jae Bok Jun 충청수학회 2019 충청수학회지 Vol.32 No.3
In the present paper, we study quasi-concircular curvature tensor satisfying certain curvature conditions on a Lorentzian β-Kenmotsu manifold with respect to the semi-symmetric semi-metric connection.
ON ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD WITH A CERTAIN CONNECTION
Ahmad, Mobin,Haseeb, Abdul,Jun, Jae-Bok,Rahman, Shamsur Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.2
In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter symmetric connections, even some of them are not introduced so far. So, in this paper, we define a quarter symmetric semi-metric connection in an almost r-paracontact Riemannian manifold and consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold with that connection.
Ahmad, Mobin,Jun, Jae-Bok,Haseeb, Abdul 대한수학회 2009 대한수학회보 Vol.46 No.3
We define a quarter symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, noninvariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection.
QUASI-CONCIRCULAR CURVATURE TENSOR ON A LORENTZIAN β-KENMOTSU MANIFOLD
Ahmad, Mobin,Haseeb, Abdul,Jun, Jae Bok Chungcheong Mathematical Society 2019 충청수학회지 Vol.32 No.3
In the present paper, we study quasi-concircular curvature tensor satisfying certain curvature conditions on a Lorentzian ${\beta}$-Kenmotsu manifold with respect to the semi-symmetric semi-metric connection.
Ahmad, Mobin,Haseeb, Abdul,Ozgur, Cihan Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.3
We define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection.
Khan, Firoz,Baek, Seong-Ho,Kaur, Jasmeet,Fareed, Imran,Mobin, Abdul,Kim, Jae Hyun Springer US 2015 NANOSCALE RESEARCH LETTERS Vol.10 No.1
<P>In this paper, we present an optical model that simulates the light trapping and scattering effects of a paraboloid texture surface first time. This model was experimentally verified by measuring the reflectance values of the periodically textured silicon (Si) surface with the shape of a paraboloid under different conditions. A paraboloid texture surface was obtained by electrochemical etching Si in the solution of hydrofluoric acid, dimethylsulfoxide (DMSO), and deionized (DI) water. The paraboloid texture surface has the advantage of giving a lower reflectance value than the hemispherical, random pyramidal, and regular pyramidal texture surfaces. In the case of parabola, the light can be concentrated in the direction of the Si surface compared to the hemispherical, random pyramidal, and regular pyramidal textured surfaces. Furthermore, in a paraboloid textured surface, there can be a maximum value of 4 or even more by anisotropic etching duration compared to the hemispherical or pyramidal textured surfaces which have a maximum <I>h</I>/<I>D</I> (depth and diameter of the texture) value of 0.5. The reflectance values were found to be strongly dependent on the <I>h</I>/<I>D</I> ratio of the texture surface. The measured reflectance values were well matched with the simulated ones. The minimum reflectance value of ~4 % was obtained at a wavelength of 600 nm for an <I>h</I>/<I>D</I> ratio of 3.75. The simulation results showed that the reflectance value for the <I>h</I>/<I>D</I> ratio can be reduced to ~0.5 % by reducing the separations among the textures. This periodic paraboloidal structure can be applied to the surface texturing technique by substituting with a conventional pyramid textured surface or moth-eye antireflection coating.</P>