Zoll surface

A Zoll surface, named after Otto Zoll, (a student of David Hilbert's), is a surface homeomorphic to the 2-sphere, with a Riemannian metric all of whose geodesics are closed and of equal length.

References

*Besse, A.: "Manifolds all of whose geodesics are closed", "Ergebisse Grenzgeb. Math.", no. 93, Springer, Berlin, 1978.
*Funk, P.: "Über Fläschen mit lauter geschlossenen geodätischen Linien". "Mathematische Annalen" 74 (1913), 278–300.
*Guillemin, V.: "The Radon transform on Zoll surfaces". "Advances in Mathematics" 22 (1976), 85–119.
*Lebrun, C.; Mason, L.: "Zoll manifolds and complex surfaces". "Journal of Differential Geometry" 61 (2002), no. 3, 453–535.
*Zoll, Otto; Ueber Flächen mit Scharen geschlossener geodätischer Linien. (German) Math. Ann. 57 (1903), no. 1, 108--133.