John Downes (regicide) 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; family had moved southwards from Cheshire to Warwickshire. They were said to be able to trace their Cheshire lineage back to 864 AD, according to John Parsons Earwaker's "History" of East Cheshire families. It is said that when the King came hunting in Macclesfield Forest, a Downes would hold the King's stirrup, whilst he mounted and Lord Stanley would
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