This question is from Differential Geometry L N and M are th

This question is from \"Differential Geometry\"

L, N and M are the second fundamental coefficients.

Assume t hat the first fundamental form of a surface patch is du^2 + dv^2. and L. N, M are constant. Determine which values of L, M. N are possible. For every non-negative real number a find a surface patch with the first fundamental form du^2 + dv^2 and the second fundamental form adu^2.

Solution

(a) L=1, M=0, N=1

(b)