Daniel Condurache

Finite Weil Jets, Identity Transfer, and the Exponential Geometry of Proper Orthogonal Tensors

Let $\mathbb{A}=\mathbb{R}1_{\mathbb{A}}\oplus\mathfrak{m}$ be a Weil algebra with $\mathfrak{m}^{N+1}=0$. We study the exponential geometry of the proper orthogonal group $\mathrm{SO}(3,\mathbb{A})$ through finite Weil prolongation. An exact Rodrigues formula is obtained for every element of $\mathfrak{so}(3,\mathbb{A...