Below picture is from the Jost's Riemannian Geometry. At last ,I don't know how get the homotopy. It is not proved that $c_s(t)$ is continue for any $s$. So I can't get the $\Gamma(t,s)$ is continue.How to prove it ?
2026-03-28 15:19:55.1774711195
How to show the continuity
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