On the systole of the sphere in the proximity of the standard metric

DOI10.1007/s10711-006-9087-7zbMath1109.53044arXivmath/0601285OpenAlexW1480930081MaRDI QIDQ861670

Florent Balacheff

Publication date: 30 January 2007

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601285

zbMATH Keywords

critical point2-spheresystolestandard metricZoll metric

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Periodic orbits of vector fields and flows (37C27) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (10)

Geodesic loops and periodic geodesics on a Riemannian manifold diffeomorphic to \(S^{3}\) ⋮ A local contact systolic inequality in dimension three ⋮ Sharp systolic inequalities for Reeb flows on the three-sphere ⋮ Isosystolic genus three surfaces critical for slow metric variations ⋮ Contact geometry and isosystolic inequalities ⋮ A LOCAL OPTIMAL DIASTOLIC INEQUALITY ON THE TWO-SPHERE ⋮ A systolic inequality for geodesic flows on the two-sphere ⋮ Sharp systolic inequalities for Riemannian and Finsler spheres of revolution ⋮ A systolic-like extremal genus two surface ⋮ Open problems and questions about geodesics

Cites Work

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• Lower bounds on the energy of maps
• Area and the length of the shortest closed geodesic
• Simple closed geodesics on convex surfaces
• The Radon transform on Zoll surfaces
• On the volume of manifolds all of whose geodesics are closed
• Some inequalities in certain nonorientable Riemannian manifolds
• Filling Radius and Short Closed Geodesics of the $2$-Sphere
• The length of a shortest closed geodesic and the area of a 2-dimensional sphere

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