Let M be a surface in R² oriented by a unit normal vector

Last updated: 8/7/2022

Let M be a surface in R² oriented by a unit normal vector field U = g₁U₁ + g₂U₂ +g₃U₃ Then the Gauss map G: M->Σ of M sends each point p of M to the point (g₁(p), g₂(p), g₃(p)) of the unit sphere Σ. For each of the following surfaces, describe G(M) of the Gauss map in the sphere Σ: (a) Cylinder, x² + y² = r² (b) Cone, z = √(x² + y²) (c) Plane, x+y+z=0 (d) Sphere, (x - 1)² + y² + (x + 2)² = 1 This is a Differential Geometry problem.