Publication: The homogeneous geometries of real hyperbolic space
Loading...
Full text at PDC
Publication Date
2013-05
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Birkhauser Verlag AG
Citations
Exportar
Abstract
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components.
Description
UCM subjects
Unesco subjects
Keywords
Citation
W. Ambrose and I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J. 25 (1958), 647–669.
A. L. Besse, Einstein manifolds, Brgebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Vol. 10, Springgr, Berlin, Heidelberg and New York, 1987.
J. Bochnak, M. Coste, and M.-F. Roy, Géométric algébrique réelle, Ergsbnisse der Mathematik und ihrer Grenzgebiete, 3, Folge, Vol. 12, Springer-Verlag, Berlin, 1987.
M. Castrillón López, P. M. Gadea, and A. F. Swann, Homogeneous structures on real and complex hyperbolic spaces, Illinois J. Math. 53 (2009), no. 2, 561–574.
K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33–65.
A. M. Pastore, On the homogeneous Riemannian structures of type F 1 ⊕F 3 Geom. Dedicata 30 (1989), no. 2, 235–246.
A. M. Pastore, Canonical connections with an algebraic curvature tensor field on naturally reductive spaces, Geom. Dedicata 43 (1992), no. 3, 351–361.
A. M. Pastore, Homogeneous representations of the hyperbolic spaces related to homogeneous structures of class F 1 ⊕F 3 , Rend. Mat. Appl. (7) 12 (1992), no. 2, 445–453.
A. M. Pastore and F. Verroca, Some results on the homogeneous Riemannian structures of class F 1 ⊕F 2 , Rend. Mat. Appl. (7) 11 (1991), no. 1, 105–121,
F. Tricerri and L. Vanhecke, Homogeneous structures on Riemannian manifolds, London Mathematical Society Lecture Note Series, Vol. 83, Cambridge University Press, Cambridge, 1983.
D. Witte, Cocompact subgroups of semisimple Lie groups, Lie algebras and related topics. Proceedings of the conference held at the University of Wisconsin, Madison, Wisconsin, May 22-June 1, 1988 (Georgia Benkart and J. Marshall Osborn, eds.), Contemp. Math., Vol. 110, American Mathematical Society, Providence, RI, 1990, pp. 309–313.