Inoguchi Junichi

We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional non-unimodular Lie group with left invariant metric. This work together with our previous papers yield a complete classification of Grassmann geometry of orbit t...

弾性エネルギーの臨界点である平面曲線は弾性曲線とよばれる．弾性曲線はmKdV 方程式と深く関連し，実際，平面曲線の等周変形を記述するmKdV 方程式の進行波解から定まる曲線が弾性曲線である．本稿では相似幾何学の枠組みを用いて工業意匠設計で用いられている対数型美的曲線（LAC）とその一般化を考察し，それらが平面曲線の等角変形を記述するBurgers 方程式の定常解として特徴付けられること，および適当なエネルギーの臨界点として定式化できることを報告する．この結果は，LAC が弾性曲線の相似幾何...

The class of log-aesthetic curves includes the logarithmic spiral, clothoid, and involute of a circle. Although most of these curves are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform ...

The purpose of the present paper is to give an explicit form of the finite gap solutions to the Tzitzeica equation (2D Toda equation of type A_2^2) in terms of Riemann theta function. We give explicit expressions of proper affiene spheres derived ...

The normal Gauss map of a minimal surface in the model space Sol of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.

We give a classification of parallel surfaces in the groups of rigid motions of Minkowski plane and Euclidean plane, equipped with a general left-invariant metric. Our result completes the classification of parallel surfaces in the eight three-dim...

We complete the classification of surfaces with parallel second fundamental form in all three-dimensional homogeneous spaces.

We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional unimodular Lie group with left invariant metric, that is, it is one of the 3-dimensional commutative Lie group, the 3-dimensional Heisenberg group, the groups of...

We generalize the Ueno-Nakamura theory and the Uhlenbeck-Segal theory for harmonic maps of Riemann surfaces into compact semi-simple Lie groups to those of (affine) harmonic maps into general Lie groups with torsion free bi-invariant connection in...

In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Bur...

A curve is considered fair if it consists of continuous and few monotonic curvature segments. Polynomial curves such as Bézier and B-spline curves have complex curvature function, hence the curvature profile may oscillate easily with a little twea...

It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe it. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization princip...

We generalize the Uhlenbeck-Segal theory for harmonic maps into compact semi-simple Lie groups to general Lie groups equipped with torsion free bi-invariant connection.