Inoguchi, Jun-ichi;Ziatdinov, Rushan;Miura, Kenjiro T.
Japan Journal of Industrial and Applied Mathematics 36(1) 239-259 2019年1月 [査読有り]
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 ...
Journal of Physics Communications 2 2018年11月 [査読有り]
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 ...
Proceedings of the American mathematical Society 136(6) 2209-2216 2008年5月 [査読有り]
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.
Parallel surfaces in the motion groups E(1,1) and E(2)
Inoguchi, Jun-ichi;Van der Veken, Joeri
Bulletin of the Belgian Mathematical Society - Simon Stevin 14(2) 321-332 2007年6月 [査読有り]
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 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...
The hidden symmetry of chiral fields and the Riemann-Hilbert problem, revisited
井ノ口, 順一
京都大学数理解析研究所講究録 2071 1-16 2018年4月
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...
Computer-Aided Design and Applications 15(2) 256-263 2017年10月 [査読有り]
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...
Dorfmeister, Josef F;Inoguchi, Jun-ichi;Kobayashi, Shimpei
Advances in Mathematics 298 207-253 2016年8月 [査読有り]
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.
