February 16th (Thu.)

Mini-Workshop "Differential Geometry, Integrable Systems, and Shape Generation"

• 11:00 - 12:00

  A construction of explicit formula of the motion of Kaleidocycles using elliptic theta functions

  Shota Shigetomi (Kyushu University)

  Abstract: We construct an explicit formula for the isoperimetric deformation of a discrete space curve preserving its torsion angle. We expect that the formula describes a motion of Kaleidocycles.

• 12:15 - 13:15

  On the solutions of sine-Gordon equation and their discretization

  Seiichi Udagawa (Nihon University)

  We show Jacobi elliptic solutions of semi-discrete sine-Gordon and discrete sine-Gordon equations based on the solutions of the sine-Gordon equation. We also show the relation with the Riemann theta solutions described by Bobenko and Pinkall (J. Differential Geometry 43(1996), 527-611)

• Lunch

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• 15:30 - 16:30

  Geometric shape generation of shell membrane and truss structures

  Yoshiki Jikumaru (Kyushu University)

  Abstract: It is known that a transformation of a surface preserving a "good" property in classical differential geometry naturally relates to the modern soliton theory, which is known as integrable geometry. On the other hand, for a given load acting on a structure, the transformation induced by the equilibrium condition of forces and moments often can be understood by integrable geometry. In this talk, we discuss the shape generation of shell membrane and Michell truss-like structures based on integrable geometry.

• 16:45 - 17:45

  Lie sphere geometry: Is it future promising?

  Jun-ichi Inoguchi (Hokkaido University)

  Abstract: We discuss applicability of Lie-sphere, Moebius and Laguerre geometry to geometric shape generation.