• 충청수학회지
• /
• 제22권3호
• /
• pp.409-416
• /
• 2009

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for lightlike hypersurfaces M with totally umbilical screen distributions of a semi-Riemannian space form.

• 호남수학학술지
• /
• 제22권1호
• /
• pp.99-106
• /
• 2000

We prove that a certain class of real hypersurfaces in $P_3({\mathbb{C}})$ has the rigidity. Making use of this we classify all homogeneous real hypersurfaces in $P_3({\mathbb{C}})$.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제16권3호
• /
• pp.271-276
• /
• 2009

We study the geometry of screen conformal light like hypersurfaces M of a semi- Riemannian manifold M. The main result is a characterization theorem for screen conformal lightlike hypersurfaces of a semi-Riemannian space form.

• 대한수학회보
• /
• 제59권6호
• /
• pp.1595-1603
• /
• 2022

We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.

• 대한수학회보
• /
• 제60권3호
• /
• pp.705-715
• /
• 2023

In this paper, we present some new properties for p-biharmonic hypersurfaces in a Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces. We present some open problems.

• 대한수학회논문집
• /
• 제35권4호
• /
• pp.1221-1244
• /
• 2020

In this paper we consider L_K-conjecture introduced in [5, 6] for hypersurface Mⁿ in space form Rⁿ⁺¹(c) with three principal curvatures. When c = 0, -1, we show that every L₁-biharmonic hypersurface with three principal curvatures and H₁ is constant, has H₂ = 0 and at least one of the multiplicities of principal curvatures is one, where H₁ and H₂ are first and second mean curvature of M and we show that there is not L₂-biharmonic hypersurface with three disjoint principal curvatures and, H₁ and H₂ is constant. For c = 1, by considering having three principal curvatures, we classify L₁-biharmonic hypersurfaces with multiplicities greater than one, H₁ is constant and H₂ = 0, proper L₁-biharmonic hypersurfaces which H₁ is constant, and L₂-biharmonic hypersurfaces which H₁ and H₂ is constant.

• 대한수학회보
• /
• 제34권3호
• /
• pp.459-468
• /
• 1997

The purpose of this paper is to give some characterizations of homogeneous real hypersurfaces of type A in complex space forms $M_n(c), c \neq 0$, in terms of Lie derivatives.

• East Asian mathematical journal
• /
• 제30권1호
• /
• pp.15-22
• /
• 2014

In this paper, we study lightlike hypersurfaces M of semi-Riemannian manifolds $\bar{M}$ of quasi-constant curvatures. Our main result is a characterization theorem for screen homothetic Einstein lightlike hypersurfaces of a Lorentzian manifold of quasi-constant curvature subject such that its curvature vector field ${\zeta}$ is tangent to M.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제20권1호
• /
• pp.25-35
• /
• 2013

In this paper, we study lightlike hypersurfaces of an indefinite Sasakian manifold $\bar{M}$. First, we construct a type of lightlike hypersurface according to the form of the structure vector field of $\bar{M}$, named by ascreen lightlike hypersurface. Next, we characterize the geometry of such ascreen lightlike hypersurfaces.

• Kyungpook Mathematical Journal
• /
• 제49권3호
• /
• pp.533-543
• /
• 2009

We define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection.