Geodesic
On $\mathrm{SO}(3,3)$ as the projective group of the space $\mathrm{SO}(3)$
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 5-19

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The fractional linear action of $\mathrm{SO}(3,3)$ on the projective space $\mathrm{SO}(3)$ is proven to be a (globally defined) projective action. 
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     author = {A. A. Akopyan and A. V. Levichev},
     title = {On $\mathrm{SO}(3,3)$ as the projective group of the space $\mathrm{SO}(3)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--19},
     publisher = {mathdoc},
     volume = {476},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a0/}
}
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A. A. Akopyan; A. V. Levichev. On $\mathrm{SO}(3,3)$ as the projective group of the space $\mathrm{SO}(3)$. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 5-19. http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a0/