Frenet frames and Toda systems
Abstract
It is shown that the integrability conditions of the equations satisfied by the local Frenet frame associated with a holomorphic curve in a complex Grassmann manifold coincide with a special class of nonabelian Toda equations. A local moving frame of a holomorphic immersion of a Riemann surface into a complex Grassmann manifold is constructed and the corresponding connection coefficients are calculated.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 1999
 arXiv:
 arXiv:math/9901023
 Bibcode:
 1999math......1023R
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 Mathematics  Mathematical Physics
 EPrint:
 LaTeX2e, amsart, 23 pages