Let Edu^2+2Fdudv+Gdv^2 and Ldu^2+2Mdudv+Ndv^2 be the first and second fundamental forms of a surface patch, with X=(beginsmallmatrixE&FF&Gendsmallmatrix), Y=(beginsmallmatrixL&MM&Nendsmallmatrix). Then:

(C) X^-1Y may not be symmetric, but have real eigen values

Q79Section II (Mathematics)79 of 190

The shape operator: real eigenvalues, but not always symmetric as a raw matrix

Let $Edu^2+2Fdudv+Gdv^2$ and $Ldu^2+2Mdudv+Ndv^2$ be the first and second fundamental forms of a surface patch, with $X=\left(\begin{smallmatrix}E&F\\F&G\end{smallmatrix}\right)$ , $Y=\left(\begin{smallmatrix}L&M\\M&N\end{smallmatrix}\right)$ . Then:

Pick an option to check your answer.

Keyboard: A–D answer · S solution · ←/→ previous/next