• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.253-263
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• 2019

Let M be a curvature homogeneous or ball-homogeneous non-$coK{\ddot{a}}hler$ almost $coK{\ddot{a}}hler$ 3-manifold. In this paper, we prove that M is locally isometric to a unimodular Lie group if and only if the Reeb vector field ${\xi}$ is an eigenvector field of the Ricci operator. To extend this result, we prove that M is homogeneous if and only if it satisfies ${\nabla}_{\xi}h=2f{\phi}h$, $f{\in}{\mathbb{R}}$.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.93-101
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• 1995

Let (M,g) be an n-dimensional, connected Riemannian manifold with Levi Civita connection $\nabla$ and Riemannian curvature tensor R defined by $$ R_XY = [\nabla_X, \nabla_Y] - \nabla_{[X,Y]} $$ for all smooth vector fields X, Y. $\nablaR, \cdots, \nabla^kR, \cdots$ denote the successive covariant derivatives and we assume $\nabla^0R = R$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.395-402
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• 1999

We introduce the notion of strongly k-disk homogeneous apace and establish a characterization theorem. More specifically, we prove that any analytic Riemannian manifold (M,g) of dimension n which is strongly k-disk homogeneous with 2$\leq$k$\leq$n-1 is a space of constant curvature. Its K hler analog is obtained. The total mean curvature homogeneity of geodesic sphere in k-disk is also considered.

• The Journal of Engineering Geology
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• v.31 no.3
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• pp.283-293
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• 2021

The homogeneity of the compacted ground was analyzed using drone-based remote terrain and gravity field data. Among the topographic elements calculated by the hydrological algorithm, the topographic curvature effectively showed the shape of the surface that occurred during the compaction process, and the non-uniformly compacted area could be identified. The appropriate resolution of the digital topography requires a precision of about 10 cm. Gravity field Interpretation was performed to analyze the spatial density change of the compacted ground. In the distribution of residual bouguer gravity anomaly, the non-homogeneously compacted area showed a different magnitude of gravity than the surrounding area, and the difference in compaction was identified through gravity-density modeling. From the results, it is expected that the topographic element and gravitational field analysis method can be used to evaluate the homogeneity of the compacted ground.