What does it mean for a geodesic to be orthogonal to a submanifold?

Question

I mean obviously a geodesic $c:I \rightarrow M$ is orthogonal to some tangent vector $v\in T_pM$, if $g(v, c^{'}(0))=0$ right (if $c(0)=p$) but if I have a submanifold $S \subset M$, what does it mean, if $c$ is orthogonal to $S$?

Answer 1

The geodesic $c$ is normal to $S$ if whenever $c(t)\in S$, we have $c'(t)\in T_{c(t)}S^\perp$.