• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.429-442
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• 2017

In the present paper, screen isotropic leaves on lightlike hypersurfaces of a Lorentzian manifold are introduced and studied which are inspired by the definition of isotropic immersions in the Riemannian context. Some examples of such leaves are mentioned. Furthermore, some relations involving curvature invariants are obtained.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.317-336
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• 1998

We study real hypersurfaces of a complex space form such that the Jacobi operator with respect to the structure vector field and the structure tensor $\phi$ on the real hypersurface commute.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.331-340
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• 2018

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.101-119
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• 1996

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1539-1549
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• 2014

The closed spacelike hypersurfaces with higher order mean curvature is discussed in a de Sitter space. The hypersurface is proved stable if and only if it is totally umbilical.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.253-263
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• 2001

Niebergall and Ryan posed some open questions on 3-dimensional real hypersurfaces in complex space forms. In this paper we give affirmative answers to such kind of questions.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.211-219
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• 2009

We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a certain cyclic condition.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.443-450
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• 2010

In this paper, we study the geometry of lightlike real hyper-surfaces of an indefinite Kaehler manifold. The main result is a characterization theorem for lightlike real hypersurfaces M of an indefinite complex space form $\bar{M}(c)$ such that the screen distribution is totally umbilic.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.473-486
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• 2021

We prove non-existence of real hypersurfaces with Killing structure Jacobi operator in complex projective spaces. We also classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Killing with respect to the k-th generalized Tanaka-Webster connection.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.636-645
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• 2022

We find a 1-parameter family of homogeneous structure tensors on contact hypersurfaces in Hermitian symmetric spaces. Among their associated Ambrose-Singer connections, we prove that the TanakaWebster connection is the unique pseudo-homothetically invariant connection.