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. 
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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/

[1] Arnold V. I., “Kompleksifikatsiya tetraedra i psevdoproektivnye preobrazovaniya”, Funkts. analiz i ego pril., 35:4 (2001), 1–7 | DOI | MR | Zbl