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Zoll surface
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<h2 id="see-also">See also</h2> <ul><li><a href="/facts/Funk_transform/dxFR8YgD">Funk transform</a>: The original motivation for studying the Funk transform was to describe Zoll metrics on the sphere.</li></ul> <ul><li><a href="/facts/Arthur_Besse/NDeUz75y">Besse, Arthur L.</a> (1978), <i>Manifolds all of whose geodesics are closed</i>, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 93, Springer, Berlin, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-3-642-61876-5">10.1007/978-3-642-61876-5</a></li> <li><a href="/facts/Paul_Funk/W5gGEVJJ">Funk, Paul</a> (1913), "Über Flächen mit lauter geschlossenen geodätischen Linien", <i><a href="/facts/Mathematische_Annalen/GPhGaonc">Mathematische Annalen</a></i>, 74: 278–300, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF01456044">10.1007/BF01456044</a></li> <li><a href="/facts/Victor_Guillemin/WWrvsNe0">Guillemin, Victor</a> (1976), "The <a href="/facts/Radon_transform/JskFJRMS">Radon transform</a> on Zoll surfaces", <i><a href="/facts/Advances_in_Mathematics/kXtcl4pM">Advances in Mathematics</a></i>, 22 (1): 85–119, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2F0001-8708%2876%2990139-0">10.1016/0001-8708(76)90139-0</a></li> <li><a href="/facts/Claude_LeBrun/8FuBqmHg">LeBrun, Claude</a>; Mason, L.J. (July 2002), "Zoll manifolds and complex surfaces", <i><a href="/facts/Journal_of_Differential_Geometry/X7rU5sdg">Journal of Differential Geometry</a></i>, 61 (3): 453–535, <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/math/0211021">math/0211021</a>, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.4310%2Fjdg%2F1090351530">10.4310/jdg/1090351530</a></li> <li>Zoll, Otto (March 1903). <a href="http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002259133">"Über Flächen mit Scharen geschlossener geodätischer Linien"</a>. <i><a href="/facts/Mathematische_Annalen/GPhGaonc">Mathematische Annalen</a></i> (in German). 57 (1): 108–133. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2Fbf01449019">10.1007/bf01449019</a>.</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://mathcurve.com/surfaces.gb/tannery/tannery.shtml">Tannery's pear</a>, an example of Zoll surface where all closed geodesics (up to the meridians) are shaped like a curved-figure eight.</li></ul>