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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 23 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1266934792

Digital Object Identifier
doi:10.1215/ijm/1266934792

Mathematical Reviews number (MathSciNet)
MR2594643

Zentralblatt MATH identifier
1239.53070

Subjects
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]

Citation

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. https://projecteuclid.org/euclid.ijm/1266934792


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