Learchus (regicide) and Critola, feared for his life, and wouldn’t allow Polyarchus to travel alone, finally journeying with him. During the reign of Battus III, Battus realized the instability of his kingdom and brought in a lawgiver named Demonax to reform the government. Demonax's reforms were disregarded by the successor to Battus, Arcesilaus III, who instigated yet another period of civil strife. On the deaths of Amasis II and Arcesilaus III, both states went under the thumb of Persian rule. Learchus (regicide) Learchus () was an adviser in the government of the Kingdom of Cyrenaica during the reign of king Arcesilaus II.
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