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

TL;DR

This paper classifies real rational knots and nodal curves in a specific quadric, explores their relationship with knots in projective 3-space, and constructs representatives for knots up to degree 5.

Contribution

It provides a detailed classification of real rational knots in a signature (3,2) quadric and offers explicit constructions for knots of degree up to 5.

Findings

Classified real rational knots and nodal curves in the quadric.

Established relationships between knots in the quadric and in ^{3}.

Constructed explicit representatives for knots of degree .

Abstract

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 $\mathbb{RP}^{3}$. Furthermore, a construction for the representatives of all the real rational knots of degree $\leq 5$ in the quadric is presented.