Abstract
Flat metric is a metric of zero curvature with a finite number of degenerate points. Each of degenerate points is a cone of the angle Ө. Flat metric taken together with cone singularities defines a flat structure on M. Flat structures are connected in many ways with other objects such as quadratic differential, measured foliations, interval exchange transformations, principal curvature lines and billiards in the rational polygons.
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Bibliographic Notes
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© 2001 Springer-Verlag Berlin Heidelberg
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Nikolaev, I. (2001). Flat Structures. In: Foliations on Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04524-4_13
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DOI: https://doi.org/10.1007/978-3-662-04524-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08698-4
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