• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.685-690
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• 1997

Our study focuses on the condition under which a subspace of complex projective space can become an Einstein space. We prove that a subspace becomes an Einstein space if it's codimension is less than n-1 and its curvature tensor and Ricci tensor satisfies Ryan's condition.

• 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.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.725-736
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• 1999

In the present paper we will give a characterization of homogeneous real hypersurfaces of type A1, A2 and B of a complex projective space.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.327-332
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• 2002

In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space $P_{n+1}(C)$, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q$_n$(C) or P$_n$(C).

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.595-607
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• 2003

In the previous paper [6], the author constructed hyperbolic hypersurfaces of degree $2^{n}$ in the n-dimensional complex projective space for every $n\;\geq\;3$. The purpose of this paper is to give some improvement of this result and to show some general methods of constructions of hyperbolic hypersurfaces of higher degree, which enable us to construct hyperbolic hypersurfaces of degree d in the n-dimensional complex projective space for every $d\;\geq\;2\;{\times}\;6^{n}$.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.75-85
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• 2003

Let M be 3 Semi-invariant submanifold of codimension 3 with lift-flat normal connection in a complex projective space. Further, if the mean curvature of M is constant, then we prove that M is a real hypersurface of a complex projective space of codimension 2 in the ambient space.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.243-257
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• 1998

The purpose of this paper is to give some characterizations of $n$-dimensional CR-submanifolds with ($n-1$) CR-dimension immersed in a complex projective space $CP^{\frac{n+2}{2}}$, in terms of the Riemannian curvature tensor R.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.265-275
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• 2001

In the previous paper we studied n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space CP(sup)(n+p)/2, and especially determined such submanifolds under curvature conditions related to vertical direction; In the present article we determine such submanifolds under curvature conditions related to horizontal directions.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.575-586
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• 2001

The purpose of this paper is to study n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space $CP^{(n+p)/2}$, and especially to determine such submanifolds under some curvature conditions.