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Answer by Tapio Rajala for Geodesics intersecting a submanifold
No, take $N = S^1$, $U = \mathbb{R}^2$ and a suitable collection of line-segments parallel to an axis (for example).Edit: To respond to the question in the comment: even if we assume the intersections...
View ArticleGeodesics intersecting a submanifold
Let $U$ be an open subset in $R^n$ and let $N$ be a $C^1$-submanifold. We have a family of geodesics $\gamma:[0,1]\rightarrow U$ in U with respect to the euclidian metric. Each geodesic is parametrized...
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