Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 26J / e / Solution

For a unit-speed spherical curve,the normal component is $-\alpha$ because
$\alpha \cdot \dot{t}=-1$, and the tangential normal component is the definition of ${\kappa }_g$. If ${\kappa }_g$ is constant, thenMoreover $e\cdot \alpha ={\kappa }_g$. Hence the whole curve lies in the fixed planeso it is planar.