• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.183-205
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• 2024

In this paper, for an m-dimensional (m ≥ 5) complete non-compact submanifold M immersed in an n-dimensional (n ≥ 6) simply connected Riemannian manifold N with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of M, the norm of its weighted mean curvature vector |H_f| and the weighted real-valued function f, we can obtain: • several one-end theorems for M; • two Liouville theorems for harmonic maps from M to complete Riemannian manifolds with nonpositive sectional curvature.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.771-780
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• 2012

We study biminimal curves in 2-dimensional Riemannian manifolds of constant curvature.

• Journal of the Korean Mathematical Society
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• v.29 no.1
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• pp.55-62
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• 1992

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1101-1114
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• 1996

In Riemannian geometry, it is one of the important things to study the topological or geometric invariants of manifolds since they characterize the topology of manifolds.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.365-371
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• 1997

We prove some relation of volume with the covering radius of Riemannian manifolds and reprove well-known sphere rigidity theorems by using it.

• Korean Journal of Mathematics
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• v.3 no.2
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• pp.223-231
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• 1995

• Communications of the Korean Mathematical Society
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• v.3 no.1
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• pp.93-98
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• 1988

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.613-618
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• 1996

In this paper, M will always denote an n- dimensional complete Riemannian manifold and $\omega_n$ is the volume of $S^n$.

• Communications of the Korean Mathematical Society
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• v.8 no.3
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• pp.489-497
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• 1993

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.33-46
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• 2001

The purpose of this paper is to study totally umbilical coisotropic sub-manifold(M. g, SM) of a semi-Riemannian manifold(M,g)