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The 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.
@phdthesis{IshidaThesis2025,
author = {Sadashige Ishida},
title = {Symplectic-prequantum structures and dynamics on the codimension-2 shape space},
school = {ISTA},
year = {2025},
month = {10}
}