Showing papers by "Jun-ichi Inoguchi published in 2013"
TL;DR: In this paper, the authors studied affine biharmonic curves in model spaces of Thurston geometry except Sol and showed that every 3-dimensional Riemannian manifold with 4-dimensional isometry group admits a normal almost contact structure compatible to the metric.
Abstract: Every 3-dimensional Riemannian manifold with 4-dimensional isometry group admits a normal almost contact structure compatible to the metric. In this paper we study affine biharmonic curves in model spaces of Thurston geometry except Sol.
21 citations
TL;DR: In this paper, the authors considered the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and showed that it is possible to construct the Torsion-preserving deformation by tuning the deformation parameters.
Abstract: In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym-Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces.
17 citations
TL;DR: In this paper, integrable discretizations of the complex and real Dym equations are proposed and N-soliton solutions for both semi-discrete and fully discrete analogues of the Dym equation are also presented.
Abstract: Integrable discretizations of the complex and real Dym equations are proposed. N-soliton solutions for both semi-discrete and fully discrete analogues of the complex and real Dym equations are also presented.
9 citations
01 Dec 2013
8 citations
TL;DR: In this paper, it was shown that the normal Gauss map for a surface in the 3-sphere with Gauss curvature k ≥ 1 is Lorentz harmonic with respect to the metric induced by the second fundamental form if and only if k ≥ 0.
Abstract: In this paper we study constant positive Gauss curvature $K$ surfaces in the 3-sphere $S^3$ with $0
6 citations
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TL;DR: In this paper, the authors investigated periodic magnetic curves in elliptic Sasakian space forms and obtained a quantization principle for periodic magnetic flowlines on Berger spheres, and gave a criterion for periodicity of magnetic curves on the unit sphere.
Abstract: It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe them. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criterion for periodicity of magnetic curves on the unit sphere ${\mathbb{S}}^3$.
3 citations