Real rational knots in the quadric of signature~$(3,2)$

We study the space of real rational curves of low degree in the quadric of signature $(3,2)$ and provides a classificaton of real rational knots and nodal curves. Apart from the classification, we also study the relationship between the real rational knots in the quadric and the real rational knots in ${\mathbb{R}\mathbb{P}}^3$. Furthermore, a construction for the representatives of all the real rational knots of degree $\le 5$ in the quadric is presented.