EQUATIONS OF ELASTIC HYPERSURFACES

78 SHELLS
Remark 3.15 By iteration, an identity similar in spirit to (3.47) holds for higher order
weakly tangential differential operators which are higher order polynomials of Gunter’s or
Stoke’s derivatives (cf. Lemma 3.16).
In this connection, let us also point out that the strongly tangential operator
curl S := N ∧ ∇ S = N ∧ ∇ = { M 23 , −M 13 , M 12
}
, curlS
∣
∣S = ν ∧ ∇ S (3.50)
in R 3 acting on scalar functions on S , is naturally identified with the skew-symmetric matrix
whose entries are the Stokesian derivatives, in the sense that
ν ∧ d = 1 2
3∑
M jk dx j ∧ dx k =
j,k=1
∑
1≤j