Illinois Journal of Mathematics

Homogeneous structures on real and complex hyperbolic spaces

M. Castrillón López, P. M. Gadea, and A. F. Swann

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The connected groups acting by isometries on either the real or the complex hyperbolic spaces are determined. A Lie-theoretic description of the homogeneous Riemannian, respectively Kähler, structures of linear type on these spaces is then found. On both spaces, examples that are not of linear type are given.

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Illinois J. Math., Volume 53, Number 2 (2009), 561-574.

First available in Project Euclid: 23 February 2010

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Zentralblatt MATH identifier

Primary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]


López, M. Castrillón; Gadea, P. M.; Swann, A. F. Homogeneous structures on real and complex hyperbolic spaces. Illinois J. Math. 53 (2009), no. 2, 561--574. doi:10.1215/ijm/1266934792.

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