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Condition that a tensor be the curl of a vector

1922
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Bulletin of the American Mathematical Society
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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