Let M be a surface in R oriented by a unit normal vector fieldU =...
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Algebra
Let M be a surface in R oriented by a unit normal vector fieldU = g?U? + g?U? +g?U?Then the Gauss map G: M->? of M sends each point p of M to the point (g?(p), g?(p), g?(p)) of the unit sphere ?. For each of the following surfaces, describe G(M) of the Gauss map in the sphere ?:(a) Cylinder, x + y = r(b) Cone, z = ?(x + y)(c) Plane, x+y+z=0(d) Sphere, (x - 1) + y + (x + 2) = 1This is a Differential Geometry problem.
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