Flowers on Riemannian manifolds
A \textit{minimal geodesic flower} is a bouquet of finitely many geodesic loops starting at the same point with the following property: The sum of the unit vectors at the base point tangent to all geodesic arcs directed from the base point equals zero. The author shows that on a compact Riemannian manifold of dimension \(n\) there exists a non-trivial geodesic flower consisting of at most \(2n-1\) geodesic loops. The total length of the flower is bounded from above by \(2 n! d,\) where \(d\) denotes the diameter. The work is a continuation of the author's work on \textit{geodesic nets.}
scientific article; zbMATH DE number 5963459
scientific article