Asymptotically optimal $t$-design curves on the Grassmann manifold

Clemens Karner, Martin Ehler, Pedro R. López-Gómez

Session: General

Keywords: Spherical designs, t-design curves, Grassmannian manifold

Abstract: Similarly to well-known spherical $t$-design points, we investigate $t$-design curves on the Grassmannian manifold $\operatorname{Gr_{2,4}}$. Such curves have the special property that the line integral along them integrates polynomials of degree $t$ exactly. We derive asymptotic bounds on the length of such curves based on a parametrization of $\operatorname{Gr_{2,4}}$ as $(\mathbb{S}^2\times\mathbb{S}^2)/{\pm 1}$.

Submission Number: 104