Abstract
A map 𝜙 of a metric space R in which any two points can be connected by a rectifiable curve into a metric space R’ preserves length or is equilong, if the length of any curve x(t), α≦t≦β, in R equals that of its image 𝜙x(t) in R’. For R = R’ we speak of an equilong map of R. Local isometries are special equilong maps. An equilong map is proper if it is not an isometry.
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© 1970 Springer-Verlag Berlin Heidelberg
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Busemann, H. (1970). Length Preserving Maps. In: Recent Synthetic Differential Geometry. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88057-5_3
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DOI: https://doi.org/10.1007/978-3-642-88057-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-88059-9
Online ISBN: 978-3-642-88057-5
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