In this paper we describe a non-local moving frame along a curve of pure spinors in O(2m, 2m)/P , and its associated basis of differential invariants. We show that the space of differential invariants of Schwarzian-type define a Poisson submanifold of the spinor Geometric Poisson brackets. The resulting restriction is given by a decoupled system of KdV Poisson structures. We define a generaliza...

In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that ${\cal N}=0,1,2,3,4$ can be systematically obtained as certain projections Maurer-Cartan forms superconformal groups after imposing simple conditions on them. also present Schwarzian actions defined integrals products Cartan forms. contrast with previous attempts to obtain super-Sc...

Differential equations are derived for a continous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.

Recent interest in the “memory effect” prompted us to revisit relation of gravitational waves oscillators. 50 years ago Niederer (1973) found that an isotropic harmonic oscillator with a constant frequency can be mapped onto free particle. Later Takagi (1990) has shown “time-dependent scaling” extends versus particle correspondence time-dependent when scale factor satisfies Sturm–Liouville equa...