• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1047-1065
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• 2017

The notion of a non-metric ${\phi}$-symmetric connection on semi-Riemannian manifolds was introduced by Jin [6, 7]. The object of study in this paper is generic lightlike submanifolds of an indefinite Kaehler manifold ${\bar{M}}$ with a non-metric ${\phi}$-symmetric connection. First, we provide several new results for such generic lightlike submanifolds. Next, we investigate generic lightlike submanifolds of an indefinite complex space form ${\bar{M}}(c)$ with a non-metric ${\phi}$-symmetric connection.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.311-323
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• 2014

In this paper, we construct two types of non-tangential half lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Our main result is to prove several characterization theorems for each types of such half lightlike submanifolds equipped with totally geodesic screen distributions.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.387-395
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• 1998

In this article we prove a Harnack inequality for the positive solutions of the heat equation with Neumann boundary condition for a compact Riemannian manifold with possibly non-convex boundary.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.143-150
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• 1998

In this paper, we investigate some properties of Jacobi fields and conjugate points in a complete Riemannian manifold M. Also we get a necessary and sufficient condition about a geodesic without conjugate points in the manifold with non-negative curvature.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.517-523
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• 2017

The purpose of the present paper is to study an almost generalized pseudo-Ricci symmetric manifold. The existence of such manifold is ensured by an example. Furthermore, having found, faulty example in [13], the present paper also attempts to construct a non-trivial example of an almost pseudo Ricci symmetric manifold.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.175-185
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• 2022

The purpose of this paper is to study invariant submanifolds of a Lorentzian para Kenmotsu manifold. We obtain the necessary and sufficient conditions for an invariant submanifold of a Lorentzian para Kenmotsu manifold to be totally geodesic. Finally, a non-trivial example is built in order to verify our main results.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1271-1280
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• 2023

The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized B-symmetric manifold (W CGBS)_n. We obtain a sufficient condition for a weakly cyclic generalized B-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized B-symmetric manifolds. Then we study Einstein (W CGBS)_n (n > 2). Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.

• 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.

• Journal of the Korea Computer Graphics Society
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• v.4 no.1
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• pp.11-19
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• 1998

Non-manifold topological operations such as Euler and Boolean operations provide a versatile environment for modeling domains. The implementation of these operations raises geometrical issues that need to be addressed to ensure the topological validity of the underlying model, and they uses the glue operation which provides a basic method to modify the topology of non-manifold models when vertices, edges and faces are contacting each other. Topological information such as adjacency relationships should be inferred when gluing non-manifold models. Two methods of reasoning can be employed to find the topological information : topological reasoning and geometrical reasoning. The topological method can infer the adjacency relationships by using stored topological information. On the other hand, the geometrical method can find topological ambiguities by considering the geometrical shape at the local area of gluing when the topological relations were not stored. This paper describes the geometrical reasoning method.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1203-1219
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• 2020

Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (ℓ, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (ℓ, m)-type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (ℓ, m)-type connection.