• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-16
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• 2018

In this paper, we give characteristic differential equations of a kind of projective vector fields on Finsler manifolds. Using these equations, we prove the vanishing theorem of projective vector fields on any compact Finsler manifold with the negative mean Ricci curvature, which is defined in [10]. This result involves the vanishing theorem of Killing vector fields in the Riemannian case and the work of [1, 14].

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.49-59
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• 2012

In this article, using the example of C. Camci([7]) we reconfirm necessary sufficient condition for a slant curve. Next, we find some necessary and sufficient conditions for a slant curve in a Sasakian 3-manifold to have: (i) a $C$-parallel mean curvature vector field; (ii) a $C$-proper mean curvature vector field (in the normal bundle).

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• Honam Mathematical Journal
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• v.17 no.1
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• pp.49-55
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-998
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• 2009

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, $\theta$-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant $\Theta_k$ of different kind of submanifolds of a S-space form $\tilde{M}(c)$ are obtained.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.10
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• pp.1340-1346
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• 1999

The turbulent shear flow around a surface-mounted vertical fence was investigated using the two-frame PTV system. The Reynolds number based on the fence height(H) was 2950. From this study, it is revealed that at least 400 instantaneous velocity field data are required for ensemble average to get reliable turbulence statistics, but only 100 field data are sufficient for the time-averaged mean velocity information. Various turbulence statistics such as turbulent intensities, turbulence kinetic energy and Reynolds shear stress were calculated from 700 instantaneous velocity vector fields. The fence flow has an unsteady recirculation region behind the fence, followed by a slow relaxation to the flat-plate boundary layer flow. The time-averaged reattachment length estimated from the streamline distribution is about 11.2H. There exists a region of negative Reynolds shear stress near the fence top due to the highly convex (stabilizing) streamline-curvature of the upstream flow. The large eddy structure in the separated shear layer seems to have significant influence on the development of the separated shear layer and the reattachment process.