Geodesic
Geodesic orbit Riemannian metrics on spheres
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 3, pp. 67-76

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In this paper, a complete classification of geodesic orbit Riemannian metrics on spheres $S^n$ is obtained. We also construct some explicit examples of geodesic vectors for $Sp(n+1)U(1)$-invariant metrics on $S^{4n+3}$. 
@article{VMJ_2013_15_3_a7,
     author = {Yu. G. Nikonorov},
     title = {Geodesic orbit {Riemannian} metrics on spheres},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {67--76},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_3_a7/}
}
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Yu. G. Nikonorov. Geodesic orbit Riemannian metrics on spheres. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 3, pp. 67-76. http://geodesic.mathdoc.fr/item/VMJ_2013_15_3_a7/