Moderate Killing Helices of Proper Order Four on a Complex Projective Space

Abstract

In this paper we study Killing helices, which are helices generated by Killing vector fields, of order 4 on a complex projective space whose first and third geodesic curvatures coincide. We construct a natural foliation structure on the set of all congruence classes of these helices. Our study shows that the moduli space of circles is canonically embedded into the moduli space of Killing helices of proper order 4 on a complex projective space.