Hamiltonian vector fields on a space of curves on the 3-sphere

Ismail Hossain, Md

Hamiltonian vector fields on a space of curves on the 3-sphere

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IsmailHossain_Md_Thesis.pdf(483.49 KB)

Date

2018-07-11

Authors

Ismail Hossain, Md

Abstract

This thesis reviews aspects related to the integrability of a Hamiltonian system on a space of arc length parametrized curves on the unit sphere $S^3$ in $\mathbb{R}^4$ of a fixed length $L$. In particular, we find that the flow of the Hamiltonian vector field corresponding to the total torsion function $X(s) \mapsto \displaystyle\int_o^{L} \tau(s) ds$ generates the curve shortening equation. Additionally, we show that the total torsion function belongs to a hierarchy of Poisson commuting functions.

Keywords

Mathematics

URI

http://hdl.handle.net/1993/33134

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FGS - Electronic Theses and Practica

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