Regular sets of lines in rank 3 polar spaces

Abstract

There are 6 families of finite polar spaces of rank $3$. The set of lines in a rank $3$ polar space form a rank $5$ association scheme. We determine the regular sets of minimal size in several of these polar spaces, and describe some examples. We also give a new family of Cameron--Liebler sets of generators in the polar spaces $O^{+}(10,q)$ when $q=3^h$ using a regular set of lines in $O(7,q)$.