Yoshinori MACHIDA

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We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also show the results for surfaces of constant Gaussian curvature and for developable surfaces. In particular we confirm that(More)
The classes of Monge–Ampère systems, decomposable and bi-decomposable Monge–Ampère systems, including equations for improper affine spheres and hypersurfaces of constant Gauss–Kronecker curvature are introduced. They are studied by the clear geometric setting of Lagrangian contact structures, based on the existence of Lagrangian pairs in contact structures.(More)
We give the generic classification on singularities of tangent surfaces to Legendre curves and to null curves by using the contact-cone duality between the contact 3-sphere and the Lagrange-Grassmannian with cone structure of a symplectic 4-space. As a consequence, we observe that the symmetry on the lists of such singularities is breaking for the(More)
The purpose of this study was to observe the vertical changes in unopposed maxillary first primary molars longitudinally. The subjects of this study were 17 children whose lower first primary molars had to be extracted. Space closure were prevented by crown-loop space maintainers for all these children. Plaster casts were made every 4 months for 16 to 24(More)
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