This study establishes the canonical connection and Kobayashi-Nomizu connection within the Heisenberg group (H ₃, 1) through a systematic derivation based on the Levi-Civita connection framework. Following this, explicit expressions for Killing vector fields are determined, and analytical formulae for Killing magnetic curves associated with both the canonical connection and the Kobayashi-Nomizu connection are derived.
Jiang et al. (Wed,) studied this question.