Answer to Question #271213 in Differential Geometry | Topology for yuvasri

Question #271213

if two families of geodesics surface intersect at a constant angle, prove that the surface has zero gaussian curvature.


1
Expert's answer
2021-11-25T18:21:02-0500

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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