Geodesic flow on (super-) Bott-Virasoro group and Harry Dym family

We show various Harry Dym type equations and Super Harry Dym equations, introduced by Brunelli, Das, and Popowicz [2003 Supersymmetric extensions of the Harry Dym hierarchy, J. Math. Phys. 44, 4756-4767 (2003)], follow from the geodesic flows on the Bott-Virasoro group and its supersymmetric generalization, superconformal group. In fact, their bi-Hamiltonian structures can be derived from the Lie Poisson structures on the (super-) Bott-Virasoro orbit. We also show that that m(2)KdV or Calogero-Degasperis equation is also connected to the Bott-Virasoro group. (C) 2004 American Institute of Physics.