Geodesic
Absence of three-dimensional totally geodesic submanifolds in the manifold of directions of physical space
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 173-174 
D. V. Ivanov. Absence of three-dimensional totally geodesic submanifolds in the manifold of directions of physical space. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 173-174. http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a10/
@article{ZNSL_2001_280_a10,
     author = {D. V. Ivanov},
     title = {Absence of three-dimensional totally geodesic submanifolds in the manifold of directions of physical space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {173--174},
     year = {2001},
     volume = {280},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is proved that the manifold of directions of physical space contains no three-dimensional totally geodesic submanifolds.