• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1211-1216
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• 2014

In this paper, we study the structure of m-quasi Einstein manifolds when there exists another distinct solution to the (${\lambda}$, n + m)-Einstein equation. In particular, we derive sufficient conditions for the non-existence of such solutions.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.565-568
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• 2007

We solve the asymptotic Dirichlet problem for a certain $Schr\"{o}dinger$ operator on 2-dimensional Cartan-Hadamard manifolds.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.779-788
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• 2009

In this paper we studied generalized ${\phi}$-recurrent and generalized concircular ${\phi}$-recurrent LP-Sasakian manifolds.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.813-822
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• 2021

The aim of this paper is to characterize a Kenmotsu 3-manifold whose metric is either a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton. Finally, we verify the obtained results by an example.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1283-1297
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• 2020

The goal of this paper is the introduction of hyper generalized 𝜙-recurrent (k, 𝜇)-contact metric manifolds and of quasi generalized 𝜙-recurrent (k, 𝜇)-contact metric manifolds, and the investigation of their properties. Their existence is guaranteed by examples.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1245-1254
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• 2020

The object of the present paper is to characterize Bach flat (k, 𝜇)-almost co-Kähler manifolds. It is proved that a Bach flat (k, 𝜇)-almost co-Kähler manifold is K-almost co-Kähler manifold under certain restriction on 𝜇 and k. We also characterize (k, 𝜇)-almost co-Kähler manifolds with divergence free Cotton tensor.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1113-1129
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• 2019

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1215-1231
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• 2023

The present article contains the study of D-homothetically deformed f-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.669-689
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• 2011

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions [5] are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium [32]. Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.603-614
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• 2013

In the article we show that nondieomorphic symplectic 4-manifolds which admit marked Lefschetz fibrations can share the same monodromy group. Explicitly we prove that, for each integer g > 0, every knot surgery 4-manifold in a family {$E(2)_K{\mid}K$ is a bered 2-bridge knot of genus g in $S^3$} admits a marked Lefschetz fibration structure which has the same monodromy group.