Geodesic
Pseudoquaternion Geometry
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 1, pp. 1-15

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We describe complex holomorphic transformations of a quaternion vector space taking left quaternion lines to left quaternion lines and real linear transformations of the quaternion plane simultaneously preserving the sets of left and right quaternion lines. 
@article{FAA_2002_36_1_a0,
     author = {V. I. Arnol'd},
     title = {Pseudoquaternion {Geometry}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {36},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_1_a0/}
}
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V. I. Arnol'd. Pseudoquaternion Geometry. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 1, pp. 1-15. http://geodesic.mathdoc.fr/item/FAA_2002_36_1_a0/