Geodesic
Necessary and sufficient conditions for the linearity of transformations which preserve cones
Matematičeskie zametki, Tome 6 (1969) no. 4, pp. 361-369.

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We find a criterion for the linearity of mappings, preserving equal and parallel cones, in one of the exceptional cases to which the theorem of A. D. Aleksandrov does not extend. 
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     author = {R. I. Pimenov},
     title = {Necessary and sufficient conditions for the linearity of transformations which preserve cones},
     journal = {Matemati\v{c}eskie zametki},
     pages = {361--369},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_4_a0/}
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R. I. Pimenov. Necessary and sufficient conditions for the linearity of transformations which preserve cones. Matematičeskie zametki, Tome 6 (1969) no. 4, pp. 361-369. http://geodesic.mathdoc.fr/item/MZM_1969_6_4_a0/