Let the first and second fundamental forms associated with a surface patch be respectively E,du^2+2F,du,dv+G,dv^2 and L,du^2+2M,du,dv+N,dv^2. If S=(beginsmallmatrixE&FF&Gendsmallmatrix) and T=(beginsmallmatrixL&MM&Nendsmallmatrix), then:

(B) S is non-singular and T may not be

Q79Section II (Mathematics)79 of 190

The first fundamental form is always non-singular; the second need not be

Let the first and second fundamental forms associated with a surface patch be respectively $E\,du^2+2F\,du\,dv+G\,dv^2$ and $L\,du^2+2M\,du\,dv+N\,dv^2$ . If $S=\left(\begin{smallmatrix}E&F\\F&G\end{smallmatrix}\right)$ and $T=\left(\begin{smallmatrix}L&M\\M&N\end{smallmatrix}\right)$ , then:

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