• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.475-487
• /
• 2003

A generalized even-dimensional Riemannian manifold defined by the ME-connection which is both Einstein and of the form (3.3) is called an even-dimensional ME-manifold and we denote it by $MEX_{2n}$. The purpose of this paper is to study a necessary and sufficient condition that there is an ME-connection, to derive the useful properties of some tensors, and to investigate a representation of the ME-vector in $MEX_{2n}$.

• Korea-Australia Rheology Journal
• /
• v.14 no.4
• /
• pp.175-188
• /
• 2002

We review the modeling and simulation of fiber orientation during injection molding processes of short fiber reinforced thermoplastics. Generally, a group of fibers are described in terms of probability distribution function or orientation tensor. Various closure approximation models to express higher order tensor in terms of Bower order tensors are reviewed. Rheology of fiber suspensions, multiple fiber-fiber interaction and numerical technique for the prediction of fiber orientation are also considered for concentrated situations.

• Korean Journal of Mathematics
• /
• v.19 no.1
• /
• pp.25-32
• /
• 2011

This paper is a direct continuation of [1]. In this paper we investigate some properties of ES-curvature tensor of g - $ESX_n$, with main emphasis on the derivation of several useful generalized identities involving it. In this subsequent paper, we are concerned with contracted curvature tensors of g - $ESX_n$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in g - $ESX_n$, which has a great deal of useful physical applications.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.347-354
• /
• 1997

The conharmonic transforamtion is a conformal transformation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishi and we generalize his results. In particular, we obtain a necessary and sufficient condition for the invariance of critical Riemannian metrics under the conharmonic transformation.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.447-461
• /
• 2009

In this paper we give a non-existence theorem for Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ satisfying the condition that the structure Jacobi operator $R_{\xi}$ commutes with the 3-structure tensors ${\phi}_i$, i = 1, 2, 3.

• Journal of the Korean Mathematical Society
• /
• v.40 no.6
• /
• pp.951-962
• /
• 2003

In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.819-835
• /
• 1998

The main purpose of this paper is to prove that if a real hypersurfaces M of a complex space form satisfies ${\nabla}_{\xi}S$=0 and $S{\xi}=\sigma\xi$ for some constant on $\sigma$ on M, then the structure vector field $\xi$ is principal, where S denotes the Ricci tensors of M.

• Journal of the Korean Mathematical Society
• /
• v.39 no.6
• /
• pp.821-879
• /
• 2002

Let U, V and W be complex vector spaces of dimensions 3, 3 and 4 respectively. The reductive algebraic group G = PGL(U) $\times$ PGL(W) $\times$ PGL(W) acts linearly on the projective tensor product space (equation omitted). In this paper, we show that the G-equivalence classes of the projective tensors are in one-to-one correspondence with the PGL(3)-equivalence classes of unordered configurations of six points on the projective plane.

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

• Korean Journal of Mathematics
• /
• v.19 no.4
• /
• pp.381-390
• /
• 2011

This paper is a direct continuation of [1]. In this paper we derive tensorial representations of contracted ES curvature tensors of $g-ESX_n$ and prove several generalized identities involving them. In particular, a variation of the generalized Bianchi's identity in $g-ESX_n$, which has a great deal of useful physical applications, is proved in Theorem (2.9).