The case Kp0 may arise in two ways exemplified by 1 a plane

The case K(p)=0 may arise in two ways exemplified by (1) a plane and (2) a cylinder x^2 + y^2 = 1. Discuss these in terms of normal curvature.

Solution

normal curvature of x² + y² = 1

by differentiation of above equation 2x +2y*dy/dx =0

x+y*dy/dx =0

dy/y = -dx/x

lny = -lnx +lnc

lnx +lny = lnc

ln(xy) = lnc

xy = c is normal curvature