Cameron-Liebler line classes in PG (3,q)

A Cameron-Liebler line class is a set L of lines in PG(3, q) for which there exists a number x such that |LS|=x for all spreads S. There are many equivalent properties: Theorem 1 lists eight. This paper classifies Cameron-Liebler line classes with x4 (with two exceptions). It is also shown that the study of Cameron-Liebler line classes is equivalent to the study of weighted sets of points in PG(3, q) with two weights on lines.