Question

4.25. Combine the previous result with Proposition 4.10 to prove that if a(s) is a unit speed curve with K,-0, τ 0, then α(s) lies on a sphere if and only if τ/K- . (K7sK')' (or τρ-:-(p'/t)'). PROPOSITION 4.10. Let α(s) be a unit speed curve 0. If τ whose lies sphere on a image 0, then of radius r and center m. Then K where ρ :-1/K and σ-1/τ. Hence rz-

Answer 1

He have て Consider f p2+ (p :. m it a censtont vester r 2 G) Ues on a rurfare f a sphere.