Learchus (regicide) Learchus (regicide) Learchus () was an adviser in the government of the Kingdom of Cyrenaica during the reign of king Arcesilaus II. Learchus is best known for perpetrating the murder of this very same Arcesilaus II. Little is known about Learchus, besides what is written in Plutarch's "Moralia" and the "Histories" by Herodotus, who mentions him in passing. Learchus appears to have been an early acquaintance of murder, having killed a Cyrenaean noble who was the husband of the Princess Critola and father of Queen Eryxo. When Battus II of Cyrene died, his son Arcesilaus II ascended the throne, along
Conformal Killing equation Conformal Killing equation In conformal geometry, the conformal Killing equation on a manifold of space-dimension "n" with metric formula_1 describes those vector fields formula_2 which preserve formula_1 up to scale, i.e. for some function formula_5 (where formula_6 is the Lie derivative). Vector fields that satisfy the conformal Killing equation are exactly those vector fields whose flow preserves the conformal structure of the manifold. The name Killing refers to Wilhelm Killing, who first investigated the Killing equation for vector fields that preserve a Riemannian metric. By taking the trace we find that necessarily formula_7. Therefore we can write the conformal Killing