Consider the surface M parametrized by σ(u, v) = (sin u cos v, sin u sin v, 3 cos u), 0 < u < π, 0 < v < 2π.
Let P = (sqrt(2)/2, sqrt(2)/2, 0) in M. Find the matrix Sp with respect to the basis {σu(P), σv(P)} in TP(M).
I've already shown that the surface is regular, and I know how to compute the first and second fundamental forms to stick those in the shape operator. My question is about the basis. When calculating the forms, do I evaluate the partials at P?
The professor posted the solutions, so this thread can be deleted.
Let P = (sqrt(2)/2, sqrt(2)/2, 0) in M. Find the matrix Sp with respect to the basis {σu(P), σv(P)} in TP(M).
I've already shown that the surface is regular, and I know how to compute the first and second fundamental forms to stick those in the shape operator. My question is about the basis. When calculating the forms, do I evaluate the partials at P?
The professor posted the solutions, so this thread can be deleted.
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