John Downes (regicide) being found guilty of regicide, John Downes was condemned to death in October 1660 but the sentence was commuted to life imprisonment because he had tried to intervene on the King's behalf and only signed the death warrant after being intimidated by the other commissioners. Downes spent the rest of his life a prisoner in the Tower of London. John Downes (regicide) Colonel John Downes (1609 – c. 1666) was a commissioner who signed the death warrant of Charles I of England. After the English Restoration he was found guilty of regicide and was imprisoned until he died. John Downes;
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