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NUMBER M17115
AUTHOR Seo, Aeryeong
TITLE A KOBAYASHI PSEUDO-DISTANCE FOR HOLOMORPHIC BRACKET GENERATING DISTRIBUTIONS
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JOURNAL TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019
ABSTRACT We generalize the Kobayashi pseudo-distance to complex manifolds which admit holomorphic bracket generating distributions. The generalization is based on Chow's theorem in sub-Riemannian geometry. Let G be a linear semisimple Lie group. For a complex G-homogeneous manifold M with a G-invariant holomorphic bracket generating distribution D, we prove that (M, D) is Kobayashi hyperbolic if and only if the universal covering of M is a canonical flag domain and the induced distribution is the superhorizontal distribution.
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