I have currently opted for a course titled Differential Geometry of Curves and Surfaces for which my instructor is referring to Montiel and Ros' Curves and Surfaces. Having finished Chapter 1, I am still not getting how to solve the exercises given. For example:
(18) Let $\alpha:I \rightarrow \mathbb{R}^3$ a curve parametrized by arc length (p.b.a.l) with positive curvature.Then $\alpha$ is an arc of a circle if and only if it has constant curvature and it's trace is contained in a sphere.
From where should one start to solve such problems?