Geodesic
The Bonnet-Meyers theorem is true for Riemann Hilbert Manifolds.
Mathematica Scandinavica, Tome 58 (1986), pp. 236-238
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Mots-clés : infinite dimensional manifolds, Riemannian geometry 
@article{MS2_1986__58_166980,
     author = {Lars Andersson},
     title = {The {Bonnet-Meyers} theorem is true for {Riemann} {Hilbert} {Manifolds.}},
     journal = {Mathematica Scandinavica},
     pages = {236--238},
     year = {1986},
     volume = {58},
     zbl = {0588.58003},
     url = {http://geodesic.mathdoc.fr/item/MS2_1986__58_166980/}
}
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Lars Andersson. The Bonnet-Meyers theorem is true for Riemann Hilbert Manifolds.. Mathematica Scandinavica, Tome 58 (1986), pp. 236-238. http://geodesic.mathdoc.fr/item/MS2_1986__58_166980/