• 대한수학회논문집
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• 제35권4호
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• pp.1255-1267
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• 2020

The class of isotropic almost complex structures, J_𝛿,𝜎, define a class of Riemannian metrics, g_𝛿,𝜎, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics g_𝛿,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for J_𝛿,𝜎.

• 대한수학회보
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• 제49권3호
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• pp.655-667
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• 2012

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $M$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $n$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

• 대한수학회논문집
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• 제37권2호
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• pp.585-594
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• 2022

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ², g₀) × (N, ${\tilde{g}}$), where g₀ is the flat metric on ℝ² and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × W with the warped product metric $ds^2+h(s)^2{\tilde{g}}$, where ${\tilde{g}}$ is a constant curved metric on a three dimensional manifold W.

• Kyungpook Mathematical Journal
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• 제4권2호
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• pp.39-48
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• 1961

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.921-928
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• 1999

K. Kenmotsu introduced and studied the so-called Kenmotsu manifold related to the warped product space. In this paper we charac-terize a Kenmotsu Manifold using the fibred Riemannian space.

• 호남수학학술지
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• 제43권3호
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• pp.539-545
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• 2021

In this paper, we study some symmetric and recurrent conditions of nearly cosymplectic manifolds. We prove that Ricci-semisymmetric and Ricci-recurrent nearly cosymplectic manifolds are Einstein and conformal flat nearly cosymplectic manifold is locally isometric to Riemannian product ℝ × N, where N is a nearly Kähler manifold.

• 호남수학학술지
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• 제43권2호
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• pp.289-304
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• 2021

In this paper, we establish several geometric characterizations focusing on the relationship between the squared norm of the second fundamental form and the warping function of SCR-lightlike warped product submanifolds in an indefinite Kaehler manifold. In particular, we find an estimate for the squared norm of the second fundamental form h in terms of the Hessian of the warping function λ for SCR-lightlike warped product submanifolds of an indefinite complex space form. Consequently, we derive an optimal inequality, namely $${\parallel}h{\parallel}^2{\geq}2q\{{\Delta}(ln{\lambda})+{\parallel}{\nabla}(ln{\lambda}){\parallel}^2+\frac{c}{2}p\}$$, for SCR-lightlike warped product submanifolds in an indefinite complex space form. We also provide one non-trivial example for this class of warped products in an indefinite Kaehler manifold.

• 호남수학학술지
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• 제38권2호
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• pp.359-366
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• 2016

Let H be the 3-dimensional Heisenberg group, ($G=H{\times}S^1$, g) a product Riemannian manifold of Riemannian manifolds H and S with arbitrarily given left invariant Riemannian metrics respectively, and ${\Gamma}$ the discrete subgroup of G with integer entries. Then, on the Riemannian manifold ($M:=G/{\Gamma}$, ${\Pi}^*g=\bar{g}$), ${\Pi}:G{\rightarrow}G/{\Gamma}$, we evaluate the scalar curvature and the Ricci curvature.

• 충청수학회지
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• 제24권2호
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• pp.171-185
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• 2011

In this paper, when N is a compact Riemannian manifold of class (C), we consider the nonexistence of some warping functions on Riemannian warped product manifolds $M=[a,\;{\infty}){\times}_fN$ with prescribed scalar curvatures.

• 대한수학회보
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• 제35권3호
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• pp.491-501
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• 1998

If N is any cartesian product of a closed simply connected n-manifold $N_1$ and a closed aspherical m-manifold $N_2$, then N is a codimension 2 fibrator. Moreover, if N is any closed hopfian PL n-manifold with $\pi_iN=0$ for $2 {\leq} i < m$, which is a codimension 2 fibrator, and $\pi_i N$ is normally cohopfian and has no proper normal subroup isomorphic to $\pi_1 N/A$ where A is an abelian normal subgroup of $\pi_1 N$, then N is a codimension m PL fibrator.