• Communications of the Korean Mathematical Society
• /
• v.26 no.4
• /
• pp.635-647
• /
• 2011

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$. We provide several new results on such a real half lightlike submanifold M by using the F-structure of M induced by the almost complex structure J of $\bar{M}$.

• Communications of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.107-118
• /
• 2017

In this paper we study CR-submanifolds of maximal CR-dimension by investigating extrinsic behaviors of integral curves of characteristic vector field on them. Also we consider the notion of ruled CR-submanifold of maximal CR-dimension which is a generalization of that of ruled real hypersurface and find some characterizations of ruled CR-submanifold of maximal CR-dimension concerning extrinsic shapes of integral curves of the characteristic vector field and those of CR-Frenet curves.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.395-406
• /
• 2007

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for an integral submanifold of an S-space form. By polarization, we get a basic inequality for Ricci tensor also. Equality cases are also discussed. By giving a very simple proof we show that if an integral submanifold of maximum dimension of an S-space form satisfies the equality case, then it must be minimal. These results are applied to get corresponding results for C-totally real submanifolds of a Sasakian space form and for totally real submanifolds of a complex space form.

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

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1285-1296
• /
• 2010

We give criterions for a submanifold to be an extrinsic sphere and to be a totally geodesic submanifold by observing some Frenet curves of order 2 on the submanifold. We also characterize constant isotropic immersions into arbitrary Riemannian manifolds in terms of Frenet curves of proper order 2 on submanifolds. As an application we obtain a characterization of Veronese embeddings of complex projective spaces into complex projective spaces.

• Honam Mathematical Journal
• /
• v.42 no.3
• /
• pp.621-643
• /
• 2020

Depending on the characteristic vector filed ζ, a generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection has various characterizations. In this paper, when the characteristic vector filed ζ belongs to the screen distribution S(TM) of M, we provide some characterizations of (Lie-) recurrent generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection. Moreover, we characterize various generic lightlike submanifolds in an indefinite complex space form ${\bar{M}}$ (c) with a semi-symmetric metric connection.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.169-178
• /
• 2019

Let $M^{2n+1}$, $n{\geq}1$, be a smooth manifold with a pseudoconvex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $M={\mathcal{S}}_0{\supset}{\mathcal{S}}_1{\supset}{\cdots}{\supset}{\mathcal{S}}_n$, where $S_q$ is the set of points where the Levi-form has nullity ${\geq}q$. We prove that ${\mathcal{S}}{_q}^{\prime}s$ are locally given as common zero sets of the coefficients $A_j$, $j=0,1,{\ldots},q-1$, of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coefficients $A_j$.

• Kyungpook Mathematical Journal
• /
• v.34 no.1
• /
• pp.95-108
• /
• 1994

• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.383-390
• /
• 2000

This paper is to show that a submanifold of codimension 2 of an odd-dimensional sphere with an almost contact metric structure is an intersection of a complex cone with generator as a normal vector and a sphere.

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