Integral curves of Killing vector fields in a complex projective space (Q2731098)

The authors consider the complex projective \(n\)-dimensional space of constant holomorphic sectional curvature \(4\) as a model space. Roughly speaking, a smooth curve \(\gamma\) in the model space is a helix when all its curvatures (in the Frenet frame) are constant and a circle when the Frenet frame has only two non-zero vectors and one constant non-zero curvature (the others are identically zero). They study several natural questions: Under which conditions is a circle in the projective space closed? For each positive \(l\) does there exist a unique closed circle whose length is \(l\) (up to isometries)? As a tool, some circles are considered as integral curves of suitable Killing vector fields. Also distance spheres and closed helices are studied.