• 호남수학학술지
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• 제42권3호
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• pp.461-476
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• 2020

The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.

• 호남수학학술지
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• 제42권3호
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• pp.601-620
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• 2020

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 curvature tensor and Ricci tensor are calculated. Also, we study the η-Ricci solitons on a Trans-Sasakian Manifolds with quartersymmetric non-metric connection. Indeed, we investigated that the Ricci and η-Ricci solitons with quarter-symmetric non-metric connection satisfying the conditions ${\tilde{R}}.{\tilde{S}}$ = 0. In a particular case, when the potential vector field ξ of the η-Ricci soliton is of gradient type ξ = grad(ψ), we derive, from the η-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an example for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the η-Ricci solitons.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.571-584
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• 2020

The object of the present paper is to characterize generalized Ricci recurrent (GR₄) spacetimes. Among others things, it is proved that a conformally flat GR₄ spacetime is a perfect fluid spacetime. We also prove that a GR₄ spacetime with a Codazzi type Ricci tensor is a generalized Robertson Walker spacetime with Einstein fiber. We further show that in a GR₄ spacetime with constant scalar curvature the energy momentum tensor is semisymmetric. Further, we obtain several corollaries. Finally, we cite some examples which are sufficient to demonstrate that the GR₄ spacetime is non-empty and a GR₄ spacetime is not a trivial case.

• Structural Engineering and Mechanics
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• 제70권4호
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• pp.445-455
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• 2019

Since the days of yore, plate's flexural analysis and formulation were dependent on the assumed coordinate system. In uncovering the coordinates-independent flexural interpretation, in this study, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments, in accordance with the continuum mechanics. The paper herein presents the theoretical formulations and conceptual perspectives of the Hydrostatic Method of Analysis (HM) that combines the continuum mechanics with the elasticity theory; the graphical statics and analysis; the theory of thin isotropic and orthotropic plates.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.133-166
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• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c) for c ≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉𝜙 = 𝜙R_𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in M_n(c) (⊂ M_n+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

• 대한수학회지
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• 제61권2호
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• pp.309-339
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• 2024

Let M be a real hypersurface in the complex hyperbolic quadric Q^m*, m ≥ 3. The Riemannian curvature tensor field R of M allows us to define a symmetric Jacobi operator with respect to the Reeb vector field ξ, which is called the structure Jacobi operator R_ξ = R( · , ξ)ξ ∈ End(TM). On the other hand, in [20], Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator R_ξ for a real hypersurface M in the complex hyperbolic quadric Q^m*. Furthermore, we give a complete classification of Hopf real hypersurfaces in Q^m* with such a property.

• 대한수학회지
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• 제55권5호
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• pp.1103-1129
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• 2018

In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

• 대한수학회논문집
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• 제29권2호
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• pp.331-343
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• 2014

The object of the present paper is to study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold. In this paper, we study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.389-398
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• 2018

In this paper we obtain the condition for the existence of Ricci solitons in nonflat quaternion space form by using Eisenhart problem. Also it is proved that if (g, V, ${\lambda}$) is Ricci soliton then V is solenoidal if and only if it is shrinking, steady and expanding depending upon the sign of scalar curvature. Further it is shown that Ricci soliton in semi-symmetric quaternion space form depends on quaternion sectional curvature c if V is solenoidal.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.243-257
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• 1998

The purpose of this paper is to give some characterizations of $n$-dimensional CR-submanifolds with ($n-1$) CR-dimension immersed in a complex projective space $CP^{\frac{n+2}{2}}$, in terms of the Riemannian curvature tensor R.