• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.167-182
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• 2018

In this paper, we prove the optimal inequalities for the generalized normalized ${\delta}$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (${\kappa},{\mu}$)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.

• 호남수학학술지
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• 제30권4호
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• pp.637-644
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• 2008

In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.

• 충청수학회지
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• 제28권2호
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• pp.229-241
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• 2015

In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

• Communications for Statistical Applications and Methods
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• 제18권1호
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• pp.131-136
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• 2011

The original Bates-Watts framework applies only to the complete parameter vector. Thus, guidelines developed in that framework can be misleading when the adequacy of the linear approximation is very different for different subsets. The subset curvature measures appear to be reliable indicators of the adequacy of linear approximation for an arbitrary subset of parameters in nonlinear models. Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. The accuracy of outlier tests is investigated using subset curvatures.

• Korean Journal of Mathematics
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• 제19권4호
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• pp.381-390
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• 2011

This paper is a direct continuation of [1]. In this paper we derive tensorial representations of contracted ES curvature tensors of $g-ESX_n$ and prove several generalized identities involving them. In particular, a variation of the generalized Bianchi's identity in $g-ESX_n$, which has a great deal of useful physical applications, is proved in Theorem (2.9).

• 대한수학회보
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• 제49권3호
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• pp.635-645
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• 2012

In this study, we investigate the curvature functions of ruled surface with lightlike ruling for a null curve with Cartan frame in Minkowski 3-space. Also, we give relations between the curvature functions of this ruled surface and curvature functions of central normal surface. Finally, we use the curvature theory of the ruled surface for determine differential properties of a robot end-effector motion.

• 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.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1997년도 추계 학술대회논문집
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• pp.131-135
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• 1997

Effect of wall curvature on flow characteristics is studied for mildly and strongly curved duct flows. The ducts are S-shaped, and the flow is partially blocked at the rear of the downstream. The presence of blockage in combination with curvature generates secondary flows on the concave surface; the magnitude of the secondary flow being dependent on the degree of wall curvature. Objectives are to compare the flow structures for mild and strong cases and to illuminate the changes in flow structure as the flow turns. Sensitivity on numerical solutions due to different inflow boundary conditions is also examined.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.789-799
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• 2009

In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.