Construction of submanifolds via integrable systems

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The result of the project is summarized as follows :1. Construction of a canonical projective immersion of the moduli space of marked cubic surfaces and determination of the uniformization equation2. Study of shape of the image of Schwarz map defined by the Gauss differential equation with purely imaginary exponents3. Study of transformations of projective surfaces such as projectively minimal surfaces and relation with line congruence and differential invariants; special surfaces defined by Appell's differential sytems4. Computation of the harmonic cohomology of compact symplectic nilmanifolds and construction of distinct symplectic structures on such manifolds5. Classification of CMC surfaces in H^3 and R^3 by the DPW method and explicit construction of discrete CMC surfaces6. Determination of the condition that the mean curvature of rotation surface is periodic in terms of the integral of the mean curvature7. Proposal of pluri-harmonic mapping of finite type making use of algebraic integrable systems8. Formulation of variational problem of thin films under the gravity and study of stability of solutions9. Unified method of solving sinh-Gordon, Liouville, and cosh-Gordon equation and construction of Backlund transformation of solutions10. Implementation of prime decomposition of polynomial ideals over small finite fields11. Introduction and study of the kappa function defined by j(k(r))=(r)12. Definition of the notion of flat fronts for flat surfaces with singular points in 3-dimensional hyperbolic space and development of its theory13. Proof of rigidity of projective immersions of Hermitian symmetric spaces not necessarily irreducible