Explicit formulas for the generating differential invariants and invariant differential operators for curves in two- and three-dimensional centro-equi-affine and centro-affine geometry and surfaces in three-dimensional centro-equi-affine geometry are constructed using the equivariant method of moving frames. In particular, the algebra of centro-equi-affine surface differential invariants is shown to be generated by a single second order invariant.
Bibliographical noteFunding Information:
It is a pleasure to thank Peter Giblin for inspiring me to write this paper, and for helpful advice during its genesis. This research was supported in part by NSF Grant DMS 08-07317.
Copyright 2010 Elsevier B.V., All rights reserved.
- Centro-affine geometry
- Differential invariant
- Moving frame