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In mathematics, a Zoll surface, named after Otto Zoll, is a surface homeomorphic to the 2-sphere, equipped with a Riemannian metric all of whose geodesics are closed and of equal length. While the usual unit-sphere metric on ''S''2 obviously has this property, it also has an infinite-dimensional family of geometrically distinct deformations that are still Zoll surfaces. In particular, most Zoll surfaces do not have constant curvature. Zoll, a student of David Hilbert, discovered the first non-trivial examples. ==References== *Besse, A.: "Manifolds all of whose geodesics are closed", ''Ergebisse Grenzgeb. Math.'', no. 93, Springer, Berlin, 1978. *Funk, P.: "Über Flächen 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Zoll surface」の詳細全文を読む スポンサード リンク
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