Circles in a complex projective space
In the paper are introduced the notions ``complex torsion of a circle'' and ``prime period of a closed circle'' on the complex space form \(\mathbb{C} P^n(c)\). Using the Hopf fibration \(\pi : S^{2n+1}(1) \to \mathbb{C} P^n(4)\) from a circle \(\gamma\) in \(\mathbb{C} P^n(4)\) with curvature \(k\) one gets a helix \(\widetilde {\gamma}\) with curvature \(k\) and complex torsion \(\tau\) as a horizontal lift of \(\gamma\). The main results are: Theorem 2, where differential equations for \(\widetilde{\gamma}\) are given, and the classification theorem for all circles \(\gamma\) with curvature \(k\), complex torsion \(\tau\) and its prime period.
scientific article; zbMATH DE number 871831