Let S ? R³ be a compact, orientable, regular surface with positive Gaussian curvature. Let ? be

Name: Let S ? R³ be a compact, orientable, regular surface with positive Gaussian curvature. Let ? be a simple closed geodesic in S, and let A and B be regions of S which have ? as a common boundary. Let N : S ? S² be the Gauss map of S. Prove that N(A) and N(B) have the same area.
Uploaded: 2022-06-13T20:00:13-08:00
Duration: 3 min 35 s
Channel: Sri K
Description: Let S ? R³ be a compact, orientable, regular surface with positive Gaussian curvature. Let ? be a simple closed geodesic in S, and let A and B be regions of S which have ? as a common boundary. Let N : S ? S² be the Gauss map of S. Prove that N(A) and N(B) have the same area.

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Sri K · Accepted Answer

Step 1: Given that $S$ is a compact, orientable, regular surface with positive Gaussian curvatur

Question

Let S ? R³ be a compact, orientable, regular surface with positive Gaussian curvature. Let ? be a simple closed geodesic in S, and let A and B be regions of S which have ? as a common boundary. Let N : S ? S² be the Gauss map of S. Prove that N(A) and N(B) have the same area.

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