• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1053-1068
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• 2021

We investigate the spacelike hypersurface Mⁿ with constant mean curvature (CMC) in a Lorentz Einstein manifold Lⁿ⁺¹₁, which is supposed to obey some appropriate curvature constraints. Applying a suitable Simons type formula jointly with the well known generalized maximum principle of Omori-Yau, we obtain some rigidity classification theorems and pinching theorems of hypersurfaces.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.55-60
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• 2021

Let M be a real hypersurface in a complex space form Mn(c), c ≠ 0. In this paper we prove that if the structure tensor field is Codazzi type, then M is a Hopf hypersurface. We characterize such Hopf hypersurfaces of Mn(c).

• The Pure and Applied Mathematics
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• v.28 no.3
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• pp.247-252
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• 2021

Let M be a real hypersurface in a complex space form M_n(c), c ≠ 0. In this paper, we prove that if (∇_Xϕ)Y + (∇_Yϕ)X = 0 holds on M, then M is a Hopf hypersurface, where ϕ is the tangential projection of the complex structure of M_n(c). We characterize such Hopf hypersurfaces of M_n(c).

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1191-1213
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• 2022

In this paper, we will prove the second main theorem for holomorphic curves intersecting the moving hypersurfaces in subgeneral position with index on an angular domain. Our results are an extension of the previous second main theorems for holomorphic curves with moving targets on an angular domain.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.369-378
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• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.125-133
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• 2023

We establish a characterization theorem of elliptic paraboloids in the (n+1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with extrinsic properties such as the (n+1)-dimensional volumes of regions enclosed by the hyperplanes and hypersurfaces, and the n-dimensional areas of projections of the sections of hypersurfaces cut off by hyperplanes.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.493-511
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• 2024

We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly α-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly α-Sasakian structures.

• Journal of the Korean Mathematical Society
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• v.16 no.1
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• pp.17-27
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• 1979

• East Asian mathematical journal
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• v.7 no.1
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• pp.19-22
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• 1991

• Bulletin of the Korean Mathematical Society
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• v.12 no.2
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• pp.43-49
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• 1975