A construction of closed helices with self-intersections in a complex projective space by using submanifold theory (Q1288007)

The authors study self-intersection properties of helices in complex projective spaces. This is motivated by the fact that in a standard space of constant sectional curvature a smooth curve is a helix if and only if it is generated by a Killing vector field. The authors show that this is no longer true in the case of complex projective space. They study in detail a class of helices with self-intersection which arise from a particular isometric embedding of a flat torus into complex projective space.