Geometry of curves in \(\mathbb{R}^n\) from the local singular value decomposition (Q2419017)

In this paper, the authors establish a connection between the local singular value decomposition and the geometry of $n$-dimensional curves. Also, they prove that for each $t \in I $ , the Frenet-Serret frame and the local singular vectors agree at $\gamma(t)$ and that the values of the curvature functions at $t$ can be expressed as a fixed multiple of a ratio of local singular values at $t$. To obtain this results, the authors use the approximation theory, and also the theory of monic orthogonal polynomials and moment sequences to prove a general formula for the recursion relation of a certain class of sequences of Hankel determinants. The paper consist in 6 sections. In Section 5, the authors present a very nice example adequate with the theory of the paper.