Killing vectors and magnetic curves associated to canonical connection and Kobayashi-Namizu connection in Heisenberg group

Abstract

In this paper, we define the notion of canonical connection and Kobayashi-Namizu connection in the Heisenberg group by using the Levi-Civita connection. After, we derive the expressions of Killing vector fields and obtain some explicit formulas for Killing magnetic curves associated to the canonical connection and Kobayashi-Namizu connection.