Chern's proof of Theorem 2.3 seems to be extremely confusing for me since:
(1) Since ${\alpha^{i}}$ has itself formed a coordinate, why t is necessary to describe how the one forms change?
(2) Why when $\alpha^{k}$ is constant the one - forms $\theta^{i}$ and $\theta^{i}_{j}$ are "restricted" to the curve $\alpha^{i}t$? Shouldn't it be restricted to $\alpha^{k}t$?
(3) How is (2.20) derived? It is correct on the curve $\alpha^{i}t$ but it does not seem to be obvious on other geodesic curves.
Thanks!
