Hello -
I'm trying to derive the first and second fundamental forms at any
point on an implicit surface F(x,y,z) = 0. In the article "Lecture
Note on Differential Geometry" (
http://www.cis.udel.edu/~chandra/849/Fall04/Used/dg_srinark.pdf
) , the coefficients of the first fundamental form are given (on page
14) as:
E = 1 + (Fx^2/ Fz^2)
F = FxFy/Fz
G = 1 + (Fy^2/ Fz^2)
Fx = F_x , Fy = F_y, Fz = F_z
(coefficients of the second fundamental form are too complicated to
write out here, but are given on page 15 of the article). For both
forms, I am at loss as to why both fundamental forms take the
respective forms.
Note: I suspect that these equations were not originally derived by
the author of this paper, and it is for this reason that I am asking
this question here.
Thanks,
- Olumide
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