arXiv subjects
Publications and source records attributed to Goo Ishikawa.
We solve the problem on flat extensions of a generic surface with boundary in Euclidean 3-space, relating it to the singularity theory of the envelope generated by the boundary. We give related results on Legendre surfaces with boundaries via projective duality and observe the duality on boundary singularities. Moreover we give formulae related to remote singularities of the boundary-envelope.
We consider the global symplectic classification problem of plane curves. First we give the exact classification result under symplectomorphisms, for the case of generic plane curves, namely immersions with transverse self-intersections. Then the set of symplectic classes form the symplectic moduli space which we completely describe by its global topological term. For the general plane curves with singularities, the difference between symplectomorphism and diffeomorphism classifications is clearly described by local symplectic moduli spaces of singularities and a global topological term. We introduce the symplectic moduli space of a global plane curve and the local symplectic moduli space of a plane curve singularity as quotients of mapping spaces, and we endow them with differentiable structures in a natural way.