Question

EXERCISE 4.12. For fixed øo E (0, 7), let y be a unit-speed parametriza- tion of the o-latitudinal curve in the sphere S2 (the 0-parameter curve in Example 3.24 on page 129 with = ¢o). With respect to the outward- pointing orientation of S2, show that the geodesic curvature of y is constant cot (φο). at Kg e next USurface patches EXAMPLE 3.24 (The Sphere). Recall that a its spherical coordinates (0,6), illustrated in Fig. 3.11 (left). The conver- point of S2 can be identified by 3. SURFACES sion from spherical to rectangular coordinates is encoded in the surjace ya 30 as :(0,2m) x (0, ) -S2, defined (0, ) = (sin cos 0, sin sin 0, cos ). (0,6) v(0,6) (0,6) 2T inates determine

Answer 1

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