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ON 3-DIMENSIONAL NORMAL ALMOST CONTACT METRIC MANIFOLDS SATISFYING CERTAIN CURVATURE CONDITIONS
De, Uday Chand,Mondal, Abul Kalam Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.2
The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a ${\beta}$-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.
ON GENERALIZED Z-RECURRENT MANIFOLDS
Uday Chand De,Prajjwal Pal 한국수학교육학회 2017 純粹 및 應用數學 Vol.24 No.2
The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.
Certain curvature conditions on an LP-Sasakian manifold with a coefficient α
Uday Chand De,Kadri Arslan 대한수학회 2009 대한수학회보 Vol.46 No.3
The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient α. Among others it is shown that if an LP-Sasakian manifold with a coefficient α is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient α is a spaceform.
Sasakian manifolds with quasi-conformal curvature tensor
Uday Chand De,전재복,Abul Kalam Gazi 대한수학회 2008 대한수학회보 Vol.45 No.2
The object of the paper is to study a Sasakian manifold withquasi-conformal curvature tensor.
Uday Chand De,Mohammad Nazrul Islam Khan 대한수학회 2023 대한수학회논문집 Vol.38 No.4
The aim of the present paper is to study complete lifts of a semi-symmetric non-metric connection from a Riemannian manifold to its tangent bundles. Some curvature properties of a Riemannian manifold to its tangent bundles with respect to such a connection have been investigated.
PSEUDO SYMMETRIC AND PSEUDO RICCI SYMMETRIC WARPED PRODUCT MANIFOLDS
De, Uday Chand,Murathan, Cengizhan,Ozgur, Cihan Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.4
We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.
CONFORMALLY RECURRENT SPACE-TIMES ADMITTING A PROPER CONFORMAL VECTOR FIELD
De, Uday Chand,Mantica, Carlo Alberto Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.2
In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field ${\sigma}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector ${\sigma}_j$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to ${\sigma}_j$.
ON LOCALLY 𝜙-CONFORMALLY SYMMETRIC ALMOST KENMOTSU MANIFOLDS WITH NULLITY DISTRIBUTIONS
De, Uday Chand,Mandal, Krishanu Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.2
The aim of this paper is to investigate locally ${\phi}-conformally$ symmetric almost Kenmotsu manifolds with its characteristic vector field ${\xi}$ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ${\xi}$ belongs to the $(k,\;{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$.
On Conformally at Almost Pseudo Ricci Symmetric Mani-folds
De, Uday Chand,Gazi, Abul Kalam Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.3
The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.
On Weakly Z Symmetric Spacetimes
De, Uday Chand Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.4
The object of the present paper is to study weakly Z symmetric spacetimes $(WZS)_4$. At first we prove that a weakly Z symmetric spacetime is a quasi-Einstein spacetime and hence a perfect fluid spacetime. Next, we consider conformally flat $(WZS)_4$ spacetimes and prove that such a spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field ${\rho}$. We also study $(WZS)_4$ spacetimes with divergence free conformal curvature tensor. Moreover, we characterize dust fluid and viscous fluid $(WZS)_4$ spacetimes. Finally, we construct an example of a $(WZS)_4$ spacetime.