Abstract
Certain geometric flows of curves in homogeneous plane and space geometries
are wellknown to encode scalar soliton equations through the induced
evolution of geometrical invariants of the curve.
A broad generalization of these results has been obtained on the
Hamiltonian structure of nonstretching flows of curves in homogeneous
Riemannian geometries (i.e. symmetric spaces) For any such geometry, this
gives a general geometric derivation of groupinvariant (multicomponent)
mKdV(modified Korteweg and de Vries) and SG(SineGordon) equations along
with their biHamiltonian integrability structure consisting of a shared
hierarchy of symmetries and conservation laws generated by a groupinvariant
recursion operator.
Adaptation of this derivation to nonstretching curve flows in the
quaternion projective geometry viewed as a symmetric space yield a bi
Hamiltonian hierarchy of quaternion soliton equations.
Information:
Date:  Sunday, October 4, 2009, 15:0017:00  Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
