For $n$-dimensional central affine curve flows, we
1) solve the Cauchy problem with periodic initial data and with initial data having rapidly decaying central affine curvatures,
2) construct Bäcklund transformations, a Permutability formula, and explicit solutions,
3) write down formulas for the Bi-Hamiltonian structure and conservation laws.
The first author’s research was supported in part by NSF Grant DMS-1109342.
The second author’s research was supported in part by NSF of China under Grant No. 11401327.
"$n$-dimension central affine curve flows." J. Differential Geom. 111 (1) 145 - 189, January 2019. https://doi.org/10.4310/jdg/1547607689