• Honam Mathematical Journal
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• v.27 no.2
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• pp.267-271
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• 2005

We study hypersurfaces in the Euclidean space with the following property: the tangential part of the position vector has constant length. As a result, we prove that among the connected and complete hypersurfaces in the Euclidean space, only the hypersphere centered at the origin satisfies the property.

• Kyungpook Mathematical Journal
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• v.13 no.1
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• pp.109-119
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• 1973

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.503-514
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• 1998

We want to treat this problem for real hypersurfaces in a complex hyperbolic space $J_n(C)$. Thus it seems to be natural to consider some problems concerned with the estimation of the Ricci tensor for real hypersurfaces in $H_n(C)$. In this paper we will find a new tensorial formula concerned with the Ricci tensor and give it a characterization of horospheres and geodesic hyperspheres in a complex hyperbolic space $H_n(C)$.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.665-678
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• 1997

In this paper we prove that if the minimum of the sectional curvatures of a compact n-dimensional minimal generic submanifold M of a complex projective space is 1/n, then M is the geodesic minimal hypersphere.

• 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.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.7-18
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• 2000

Let M be an n-dimensional CR submanifold CR dimension n - l of a complex projective space M. We characterize M of $\bar{M}$ in terms of an estimations of the length of the derivative of Ricci tensor of the length of Ricci tensor.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.197-206
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• 2004

We obtain some characterizations of a pseudo Ricci-parallel real hypersurface in a quaternionic projective space $QP^{n}$ and find the condition that M is locally congruent to a geodesic hypersphere of $QP^{n}$ .

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.327-335
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• 2005

For a compact and orientable minimal real hypersurface $M\;in\;QP^n$, we prove that if the minimum of the sectional curvatures of Mis 3/(4n - 1), then M is isometric to the geodesic minimal hypersphere $M_{0,n-1}^Q$.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.25-33
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• 1994

In [2] we proved that if the minimum of the sectional curvature of a compact real minimal hypersurface of CP$^{m}$ is 1/(2m-1), then M is the geodesic hypersphere. This result was generalized in [8] to the case of M is a generic submanifold with flat normal connection. The purpose of the present paper is to prove a following generalization of theorems in [2] and [8].