Geodesic
On the density of orbits through a given point in a homogeneous space
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1982), pp. 14-16 
A. N. Starkov. On the density of orbits through a given point in a homogeneous space. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1982), pp. 14-16. http://geodesic.mathdoc.fr/item/VMUMM_1982_1_a3/
@article{VMUMM_1982_1_a3,
     author = {A. N. Starkov},
     title = {On the density of orbits through a given point in a homogeneous space},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {14--16},
     year = {1982},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_1_a3/}
}
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Any dense orbit of a point on a compact submanifold is necessarily in general position.