On moving frames and Toda lattices of BKP and CKP types

Abstract

This paper is mainly concerned with the geometric formulations of Toda lattices of BKP and CKP types as evolutions of invariants and their explicit expressions. The theory for discrete curves in centro-affine geometry is constructed by using the method of a moving frame. With the help of orthogonal polynomial theory, we choose the appropriate evolutions for the curves and the evolutions induced on invariants are related to these Toda-type lattices. In addition, the explicit expressions for the discrete invariant curve flows, discrete moving frames and Maurer–Cartan invariants are provided.