×

zbMATH — the first resource for mathematics

The length of a shortest closed geodesic and the area of a \( 2\)-dimensional sphere. (English) Zbl 1098.53035
The author proves that if \(M\) is a Riemannian manifold diffeomorphic to the 2-dimensional sphere then \(l(M)\leq 4\sqrt{2}\sqrt{A}\), where \(l(M)\) and \(A\) denote the length of a shortest closed non-trivial geodesic on \(M\) and the area of \(M\), respectively. This inequality improves previous results.

MSC:
53C22 Geodesics in global differential geometry
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
PDF BibTeX XML Cite
Full Text: DOI