• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1577-1590
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• 2008

We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.729-737
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• 2006

We study Ribaucour transformations on nondegenerate local isometric immersions of Riemannian space forms into Lorentzian space forms with flat normal bundles. They can be explained by dressing actions on the solution space of Lorentzian Grassmannian systems.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.109-121
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• 2008

We determine maximal space-like hypersurfaces which are the images of subbundles of the normal bundle of m-dimensional totally geodesic space-like submanifolds of an (m + 2)-dimensional Lorentzian space form $\tilde{M}_1^{m+2}$(c) under the normal exponential map. Then we construct examples of maximal space-like hypersurfaces of $\tilde{M}_1^{m+2}$(c).

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.215-221
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• 2010

In this paper, we study the geometry of half lightlike submanifolds of a Lorentzian manifold. The main result is a characterization theorem for irrotational screen homothetic half lightlike submanifolds of a Lorentzian space form.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.225-234
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• 2010

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.163-175
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• 2013

In this paper, we prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form ($\bar{M}$(c), $\bar{g}$) with a semi-symmetric metric connection subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-zero constant.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.339-359
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• 2022

In this paper, we investigate k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using this curvatures, we establish some inequalities for screen homothetic lightlike hypersurface of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using these inequalities, we obtain some characterizations for such hypersurfaces. Considering the equality case, we obtain some results.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.198-214
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• 2023

In the present paper, we investigate homothetic motions determined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable properties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.39-50
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• 2014

In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection, whose structure vector field ${\zeta}$ is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.691-697
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• 2004

In this paper we find index form of the multiply warped product manifolds to investigate the physical properties from space-time.