A type of compact surface studied by German mathematician Otto Zoll following an idea of Darboux. It is characterized by the property that all its geodesics are closed and of the same length. A trivial example is the sphere, where the geodesics are the equatorial circles but, in general, it need not even be a surface of revolution.
Zoll Surface
See also
GeodesicThis entry contributed by Margherita Barile
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References
Berger, M. Lectures on Geodesics in Riemannian Geometry. Bombay, India: Tata Institute of Fundamental Research, 1965.Besse, A. Manifolds All of Whose Geodesics Are Closed. New York: Springer-Verlag, 1977.Darboux, G. Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitesimal. Paris: Gauthier-Villars, 1941. Reprinted by New York: Chelsea, 1972.Zoll, O. "Über Flächen mit Scharen geschlossener geodätischer Linien." Math. Ann. 57, 108-133, 1903.Referenced on Wolfram|Alpha
Zoll SurfaceCite this as:
Barile, Margherita. "Zoll Surface." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ZollSurface.html