Geometric study of Differential equations, Thurston Geometry, Geometric Shape Generation
|Keyword||Lie group, Lie algebra, Homogeneous space, Hamiltonian system, Contact structure, Thurston Geometry|
Introduction of Research
1) Differential geometric study of differential equations which posses large symmetry groups:
Those differential equations are so-called integrable systems (derived from differential geometry).
2) Differential geometric study of model spaces of 3-dimensional geometry:
According to Thurston, there are eight model spaces of 3-dimensional geometry. The model spaces of Nilgeometry, SL-geometry and Solvgeometry have natural contact structures compatible to the geometric structures. I have been studying these model spaces by virtue of contact structure and homogenous geometry.