The sectional curvature determines the metric of a (4-dimensional) spacetime, unless spacetime is a conformally flat generalized pp wave, i.e. admits coordinates such that
[G. S. Hall, Gen. Relativ. Gravitation 16, 79-88 (1984; Zbl 0535.53023)]. In the present article the authors study vector fields in conformally flat generalized pp waves which leave all sectional curvatures invariant. They show that these vector fields constitute a Lie algebra of dimension 6, 7 or 8. (The (sub) Lie algebra of Killing vector fields has dimension 6 or 7.) They calculate the structure of the Lie algebra and give a procedure to find conformally flat generalized pp waves for each possible dimension combination .