• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.391-413
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• 2018

In this paper we introduce a new tensor named semi-projective curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds $(PSPS)_n$ which recover some known results of Chaki [5]. We provide several interesting results. Among others we prove that in a $(PSPS)_n$ if the associated vector field ${\rho}$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_n$. Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.281-293
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• 2019

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.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.521-528
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• 2018

The object of the present paper is to study a decomposable $(APS)_n$ and hypersurfaces of $(APS)_n$. Also, the existence of a decomposable $(APS)_n$ is ensured by a proper example.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.367-376
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• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.893-900
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• 2023

In the present study, we consider some curvature properties of generalized B-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized B curvature tensor on Kenmostu manifold. Later we formulate generalized B pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized B ϕ-recurrent Kenmotsu manifold.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.345-353
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• 2021

The object of the present paper is to investigate the nature of Riemann solitons on generelized D-conformally deformed Kenmotsu manifold with hyper generalized pseudo symmetric curvature conditions.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.813-824
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• 2022

We study solitons of Kählerian Norden space-time manifolds and Bochner curvature tensor in almost pseudo symmetric Kählerian space-time manifolds. It is shown that the steady, expanding or shrinking solitons depend on different relations of energy density/isotropic pressure, the cosmological constant, and gravitational constant.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.623-634
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• 2011

The object of the present paper is to study N(${\kappa}$)-quasi Einstein manifolds. Existence of N(${\kappa}$)-quasi Einstein manifolds are proved. Physical example of N(${\kappa}$)-quasi Einstein manifold is also given. Finally, Weyl-semisymmetric N(${\kappa}$)-quasi Einstein manifolds have been considered.