Geodesic
On the Kobayashi Pseudometric Reduction of Homogeneous Spaces
Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 45-51

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Given any homogeneous complex manifold X = G/H, there exists a natural coset map π :G/H → G/K satisfying π (X1) = π (x2) if and only if dx(x1 x2) = 0, where dx denotes the Kobayashi pseudometric on X. Its typical fiber Z : = K/H is a connected complex submanifold of X. Also G/K has a (7-invariant complex structure, provided K satisfies a certain technical assumption (see Theorem 3). If Z is compact as well, then G/K is biholomorphic to a homogeneous bounded domain.
DOI : 10.4153/CMB-1988-007-4
Mots-clés : 32M10, 32H15 
Gilligan, Bruce. On the Kobayashi Pseudometric Reduction of Homogeneous Spaces. Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 45-51. doi: 10.4153/CMB-1988-007-4
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     title = {On the {Kobayashi} {Pseudometric} {Reduction} of {Homogeneous} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {45--51},
     year = {1988},
     volume = {31},
     number = {1},
     doi = {10.4153/CMB-1988-007-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-007-4/}
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