if two families of geodesics surface intersect at a constant angle, prove that the surface has zero gaussian curvature.
Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point:
"K=k_1k_2"
Principal curvatures at a given point of a surface measure how the surface bends by different amounts in different directions at that point.
So, if geodesics surface intersect at a constant angle, it means that surface has constant bend in one direction. So, one of its principal curvatures = 0.
So, its Gaussian curvature = 0
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