On spacelike Zoll surfaces with symmetries

Pierre Mounoud (1) , Stefan Suhr (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Fachbereich Mathematik [Hamburg]

Three explicit families of spacelike Zoll surface admitting a Killing field are provided. It allows to prove the existence of spacelike Zoll surface not smoothly conformal to a cover of de Sitter space as well as the existence of Lorentzian Möbius strips of non constant curvature all of whose spacelike geodesics are closed. Further the conformality problem for spacelike Zoll cylinders is studied.

Domaines: Géométrie différentielle [math.DG]

Pierre Mounoud, Stefan Suhr. On spacelike Zoll surfaces with symmetries. Journal of Differential Geometry, 2016, 102 (2), pp.243-284. ⟨hal-00954351⟩