Condition that a tensor be the curl of a vector

L. P. Eisenhart
1922 Bulletin of the American Mathematical Society  
It is the purpose of this note to establish the following theorem. THEOREM. A necessary and sufficient condition that a covariant skew-symmetric tensor Aij in a space of any order n be expressible in terms of n functions (pi in the form Consider first the case of 3-space. If <p 2 and <p% are any two functions such that
doi:10.1090/s0002-9904-1922-03593-8 fatcat:7froc2xjrbc4naugt5bzs6lk4a