I'm reading do Carmo's book Riemannian geometry and at the chapter 5 Jacobi fields, is this proposition.
My question is where is $a$ in the proof? At the first equal sign we should have $\frac{1}{a}$ in front of $v$ and $w.$ More over in the end we obtain that $\frac{D\overline{J}}{dt}(0)=\frac{w}{a}$ which dose not agree with $\frac{DJ}{dt}(0)=w.$ I'm missing out on something? Thanks a lot.