📘 differential geometry

1. **Problem statement:** Given a tensor field $\xi_i$ satisfying the relation $$\xi_{m,l} g_{in} + \xi_{n,l} g_{im} + g_{mn,l} \xi_i = 0,$$ prove that $$\xi_{l;m} + \xi_{m;l} = 0.

1. **Stating the problem:** We have a tensor field $\xi_i$ satisfying the relation

1. **Problem Statement:** Show that the evolute of the circle given by the equation $$x^2 + y^2 = a^2$$ reduces to a single point and explain why. 2. **Recall the definition of evo

1. The problem asks to find the radius of curvature $\rho$ at $\theta=0$ for the circle given in polar form: $$r = 2a \cos \theta.$$\n\n2. The general formula for radius of curvatu