• Honam Mathematical Journal
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• v.41 no.1
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• pp.185-195
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• 2019

In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.273-284
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• 2001

Let P be a spacelike (n-2)-dimensional submanifold of an n-dimensional Lorentz manifold M and let$\sigma$ be a P-normal null geodesic with Ric($\sigma',\sigma'$)$\geq$m, for the any given nonpositive constant m. We establish a sufficient condition such that there is a focal point of P along $\sigma$.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.783-795
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• 2019

We prove that a Lorentzian concircular structure (LCS)-manifold does not admit any null hypersurface which is tangential or transversal to its characteristic vector field. Due to the above, we focus on its ascreen null hypersurfaces and show that such hypersurfaces admit a symmetric Ricci tensor. Furthermore, we prove that there are no totally geodesic ascreen null hypersurfaces of a conformally flat (LCS)-manifold.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.81-92
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• 2008

In this paper, the trajectory scroll in 3-dimensional Minkowski space-time $E_1^3$ is given by a firmly connected oriented line moving with Cartan frame along curve. Some theorems and results between curvatures of base curve and distribution parameter of this surface are obtained. Moreover, some theorems and results related to being developable and minimal of this surface are given. And also, some relationships among geodesic curvature, geodesic torsion and the curvatures of base curve of trajectory scroll are found.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.725-743
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• 2017

We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.

• The Journal of the Convergence on Culture Technology
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• v.5 no.1
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• pp.385-388
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• 2019

Considering spherically symmetric spacetimes embedded in a 5-dimensional static Lorentzian manifold, within the large distance limit of DGP model, we study null geodesic equations. We discuss possible relations of particles following the geodesics with the gravitational waves detected recently, in comparison with the electromagnetic waves propagaing in these brane spacetimes.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.17-31
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• 1995

A Lorentzian para-Sasakian manifold M$(\varphi, \zeta, \eta, g)$ (abr. LPS-manifold) has been defined and studied in [9] and [10]. On the other hand, para-Sasakian (abr. PS)-manifolds are special semi-cosympletic manifolds (in the sense of [2]), that is, they are endowed with an almost cosympletic 2-form $\Omega$ such that $d^{2\eta}\Omega = \psi(d^\omega$ denotes the cohomological operator [6]), where the 3-form $\psi$ is the associated Lefebvre form of $\Omega$ ([8]). If $\eta$ is exact, $\psi$ is a $d^{2\eta}$-exact form, the manifold M is called an exact Ps-manifold. Clearly, any LPS-manifold is endowed with a semi-cosymplectic structure (abr. SC-structure).

• Publications of The Korean Astronomical Society
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• v.22 no.4
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• pp.103-111
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• 2007

On the formulation frameworks of linearly perturbed spacetime and weak gravitational lensing(WGL) we studied the statistical properties of a bundle of light rays propagating through stochastic gravitational wave background(SGWB). For this we considered the SGWB as tensor perturbations of linearly perturbed Friedmann spacetime. Using the solution of null geodesic deviation equation(NGDE) we related the convergence, shear and rotation deformation spectra of WGL with the strain spectra of SGWB. Adopting the astrophysical and cosmological SGWB strain spectra which were already known we investigated the approximated spectral forms of convergence, shear and rotation of WGL.