Sadashige Ishida2026-01-092026-01-092025-10-31978-3-99078-070-1https://diglib.eg.org/handle/10.2312/3607299The space of codimension-2 shapes, such as curves in 3D and surfaces in 4D, is an infinite-dimensional manifold. This thesis explores geometric structures and dynamics on this space, with emphasis on their implications for physics, particularly hydrodynamics. Our investigation ranges from theoretical studies of infinite-dimensional symplectic and prequantum geometry to numerical computation of the time evolution of shapes.enThesis