Showing papers by "Jun-ichi Inoguchi published in 2010"
Posted Content•
TL;DR: In this article, the authors construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently, and present explicit formulas in terms the $\tau$ function.
Abstract: We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms the $\tau$ function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.
29 citations
15 citations
TL;DR: In this paper, the authors investigated φ-Einstein contact Riemannian manifolds and applied it to Mathematics Subject Classification (2010) and found that φ = 0.
Abstract: φ-Einstein contact Riemannian manifolds are investigated. Mathematics Subject Classification (2010). Primary 58E20.
8 citations
4 citations
Posted Content•
TL;DR: In this article, a classification of constant mean curvature surfaces, whose Gauss map satisfies the more mild condition of vertical harmonicity, in all 3D homogeneous spaces is presented.
Abstract: It is well-known that for a surface in a 3-dimensional real space form the constancy of the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not true in general for surfaces in an arbitrary 3-dimensional ambient space. In this paper we study this problem for surfaces in an important and very natural family of 3-dimensional ambient spaces, namely homogeneous spaces. In particular, we obtain a full classification of constant mean curvature surfaces, whose Gauss map satisfies the more mild condition of vertical harmonicity, in all 3-dimensional homogeneous spaces.
1 citations
Journal Article•
TL;DR: In this paper, the authors construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently, and present explicit formulas in terms of the ε-tau function.
Abstract: We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms the $\\tau$ function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.