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Showing papers by "Jun-ichi Inoguchi published in 2015"


Journal ArticleDOI
30 Oct 2015
TL;DR: A survey on slant curves in 3D almost contact metric geometry can be found in this paper, where a 3D solvable Lie group equipped with a natural left invariant almost contact structure is considered.
Abstract: This work has two purposes. The first purpose is to give a survey on slant curves in 3-dimensional almost contact metric geometry. The second purpose is to study slant curves in 3-dimensional solvable Lie groups equipped with natural left invariant almost contact metric structure.

18 citations


Posted Content
TL;DR: In this article, a short alternative proof for the Bernstein problem in the three-dimensional Heisenberg group was presented by using the loop group technique, and the proof was used to prove the existence of an alternative solution to the problem.
Abstract: In this note we present a short alternative proof for the Bernstein problem in the three-dimensional Heisenberg group ${\rm Nil}_3$ by using the loop group technique.

1 citations


Posted Content
TL;DR: This paper presents a model of deformation of discrete space curves by the discrete nonlinear Schr\"odinger equation (dNLS), and presents explicit formulas for both NLS and dNLS flows in terms of the $\tau$ function of the 2-component KP hierarchy.
Abstract: The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schrodinger equation (NLS). In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schrodinger equation (dNLS). We also present explicit formulas for both NLS and dNLS flows in terms of the $\tau$ function of the 2-component KP hierarchy.

1 citations