• Bulletin of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.491-501
• /
• 1998

If N is any cartesian product of a closed simply connected n-manifold $N_1$ and a closed aspherical m-manifold $N_2$, then N is a codimension 2 fibrator. Moreover, if N is any closed hopfian PL n-manifold with $\pi_iN=0$ for $2 {\leq} i < m$, which is a codimension 2 fibrator, and $\pi_i N$ is normally cohopfian and has no proper normal subroup isomorphic to $\pi_1 N/A$ where A is an abelian normal subgroup of $\pi_1 N$, then N is a codimension m PL fibrator.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.457-478
• /
• 2014

In this paper, a 3D autonomous system, which has only stable or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz system and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar$\acute{e}$ map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.

• Journal of the Chungcheong Mathematical Society
• /
• v.37 no.2
• /
• pp.57-66
• /
• 2024

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in ℙ^N, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme's degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.

• Honam Mathematical Journal
• /
• v.23 no.1
• /
• pp.133-143
• /
• 2001

In this paper, we characterize some semi-invariant submanifolds of codimension 3 with almost contact metric structure (${\phi}$, ${\xi}$, g) satisfying 𝔏_ξ∇ = 0 in a nonflat complex space form, where ${\nabla}$ denotes the Riemannian connection induced on the submanifold, and 𝔏_ξ is the operator of the Lie derivative with respect to the structure vector field ${\xi}$.

• The Pure and Applied Mathematics
• /
• v.17 no.2
• /
• pp.157-165
• /
• 2010

Let (M,p) be a germ of a $C^{\infty}$ CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a $C^{\infty}$ contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in $\mathbb{C}^{n+d}$ defined by a vector valued weighted homogeneous polynomial.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.93-119
• /
• 2005

In this paper, we characterize some semi-invariant sub-manifolds of codimension 3 with almost contact metric structure ($\phi$, $\xi$, g) in a complex projective space $CP^{n+1}$ in terms of the structure tensor $\phi$, the Ricci tensor S and the Jacobi operator $R_\xi$ with respect to the structure vector $\xi$.

• 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).

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.1049-1060
• /
• 2020

We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in [26] and we also remove the condition that the second fundamental form is uniformly bounded when t ∈ (-∞, -1).

• Journal of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.109-123
• /
• 1999

In this paper we prove a reduction theorem of the codimension for real submanifold of quaternionic projective space as a quaternionic analogue corresponding to those in Cecil [4], Erbacher [5] and Okumura [9], and apply the theorem to quaternionic CR- submanifold of quaternionic projective space.

• Journal of applied mathematics & informatics
• /
• v.4 no.1
• /
• pp.249-261
• /
• 1997

We find a necessary and sufficient condition for a $\kappa$-confi-guration $\mathbb{X}$ in $\mathbb{P}^2$ to be in generic position. We obtain the number and degrees of minimal generators of some Gorenstein ideals of codimension 3 and so obtain their minimal free resolution s of these ideals.