• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.583-589
• /
• 2012

In this paper, we study locally symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$ subject to the conditions: (1) The transversal vector bundle $tr(TM)$ is parallel with respect to the connection $\bar{\nabla}$ of $\bar{M}$ and (2) M is irrotational.

• Communications of the Korean Mathematical Society
• /
• v.29 no.1
• /
• pp.141-153
• /
• 2014

In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.197-200
• /
• 2012

Concerning the integrability of almost K$\ddot{a}$hler manifolds, we prove that a compact almost K$\ddot{a}$hler locally symmetric space is K$\ddot{a}$hler if the length of the star Ricci tensor is not smaller than that of the Ricci tensor.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2001-2011
• /
• 2017

In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.133-148
• /
• 2006

This paper proposes a smoothing method for symmetric conic linear programming (SCLP). We first characterize the central path conditions for SCLP problems with the help of Chen-Harker-Kanzow-Smale smoothing function. A smoothing-type algorithm is constructed based on this characterization and the global convergence and locally quadratic convergence for the proposed algorithm are demonstrated.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.693-703
• /
• 2022

In this paper, we are concerned with the existence of infinitely many fast homoclinic solutions for the following damped vibration system $$(1){\hspace{32}}{\ddot{u}}(t)+q(t){\dot{u}}(t)-L(t)u(t)+{\nabla}W(t,u(t))=0,\;{\forall}t{\in}{\mathbb{R}},$$ where q ∈ C(ℝ, ℝ), L ∈ C(ℝ, ${\mathbb{R}}^{N^2}$) is a symmetric and positive definite matix-valued function and W ∈ C¹(ℝ×ℝ^N, ℝ). The novelty of this paper is that, assuming that L is bounded from below unnecessarily coercive at infinity, and W is only locally defined near the origin with respect to the second variable, we show that (1) possesses infinitely many homoclinic solutions via a variant symmetric mountain pass theorem.

• Journal of the Korean Mathematical Society
• /
• v.16 no.1
• /
• pp.87-93
• /
• 1979

In this note the geometric realization of a finite group of homotopy classes of self homotopy equivalences by a finite group of diffeomorphisms is investigated. In order for this to be accomplished an algebraic condition, which guarantees a certain group extension exists, must be satisfied. It is shown for a geometrically interesting class of aspherical manifolds, called injective Seifert fiber spaces over a locally symmetric space, that this necessary algebraic condition is also sufficient for geometric realization.

• Journal of the Korean Mathematical Society
• /
• v.36 no.6
• /
• pp.1145-1168
• /
• 1999

The purpose of this paper is to study the complete submanifolds with restricted space-like and time-like holomorphic bisectional curvatures in an indefinite locally symmetric K hler manifold.

• The Pure and Applied Mathematics
• /
• v.18 no.2
• /
• pp.173-183
• /
• 2011

We study half lightlike submanifolds of an indefinite Sasakian manifold. The aim of this paper is to prove the following result: If a locally symmetric half lightlike submanifold of an indefinite Sasakian manifold is totally umbilical, then it is of constant positive curvature 1. In addition to this result, we prove three characterization theorems for such a half lightlike submanifold.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.789-799
• /
• 2022

We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Alías and Meléndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.