• 대한수학회보
• /
• 제52권1호
• /
• pp.335-344
• /
• 2015

We characterize a homogeneous real hypersurface of type (A) or a ruled real hypersurface in a non-flat complex space form, respectively.

• 대한수학회보
• /
• 제47권2호
• /
• pp.341-353
• /
• 2010

In this paper, we study the geometry of screen conformal lightlike real hypersurfaces of an indefinite Kaehler manifold. The main result is a characterization theorem for screen conformal lightlike real hypersurfaces of an indefinite complex space form.

• 대한수학회보
• /
• 제26권1호
• /
• pp.69-74
• /
• 1989

Recently one of the present authors [2] asserted that a real hypersurface of a complex space form M$^{n}$ (c), c.neq.0, is of cyclic parallel if and only if AJ=JA and he showed also a complete and connected cyclic-parallel real hypersurface of M$^{n}$ (c), is congruent to type $A_{1}$, $A_{2}$ or A according as c>0 or c<0. A real hypersurface of a complex space form M$^{n}$ (c) is said to be covariantly cyclic constant if the cyclic sum of covariant derivative of the second fundamental form is constant. The purpose of the present paper is to extend theorem 3 and 4 in [2] when the hypersurfaces are of coveriantly cyclic constant, that is a real hypersurface of a complex space form M$^{n}$ (c), c.neq.0, is of covariantly cyclic constant if an only if AJ=JA, and a complete and connected covariantly cyclic constant real hypersurface of M$^{n}$ (c) is congruent to type $A_{1}$, $A_{2}$ or a according as c>0 or c<0.

• Kyungpook Mathematical Journal
• /
• 제52권3호
• /
• pp.271-278
• /
• 2012

We study some functions defined on the unit tangent space, which are formed with the second fundamental form of submanifolds of a real space form. These give an exact expression of isotropy of submanifolds in a real space form and a relationship between intrinsic invariants and extrinsic ones.

• 호남수학학술지
• /
• 제30권3호
• /
• pp.535-550
• /
• 2008

Let M be a real hypersurface of a complex space form with almost contact metric structure $({\phi},{\xi},{\eta},g)$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant and not equal to -c/24 on M, where c is a constant holomorphic sectional curvature of a complex space form.

• 대한수학회보
• /
• 제44권3호
• /
• 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.

• 대한수학회지
• /
• 제32권2호
• /
• pp.161-170
• /
• 1995

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.

• 대한수학회보
• /
• 제47권4호
• /
• pp.701-714
• /
• 2010

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold. The main result is a characterization theorem for screen conformal real half lightlike submanifolds of an indefinite complex space form.

• 대한수학회논문집
• /
• 제13권2호
• /
• pp.317-336
• /
• 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.

• 대한수학회논문집
• /
• 제25권3호
• /
• pp.443-450
• /
• 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.