| Theme | Geometric Structure, Geometric study of Differential equations, Thurston Geometry, Geometric Shape Generation |
| Field | Geometry |
| 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 homogeneous geometry.
Representative Achievements
Magnetic Jacobi fields in 3-dimensional Sasakian space forms, J. Inoguchi and M. I. Munteanu, The Journal of Geometric Analysis, 32, Article number 96 (2022)
A loop group method for affine harmonic maps into Lie groups, J.F. Dorfmeister, J. Inoguchi and S.-P. Kobayashi, Advances in Mathematics 298, 207-253 (2016)
Constant mean curvature surfaces in hyperbolic 3-space via loop groups, J.F. Dorfmeister, J. Inoguchi and S.-P. Kobayashi, J. Reine Angew. Math. 686, 1-36 (2014).
Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles, J. Inoguchi, Y. Jikumaru, K. Kajiwara, K. T. Miura, W. K. Schief, Computer Aided Geometric Design 105 (2023) Article Number 102233
