scholarly journals Tempered reductive homogeneous spaces

2015 ◽  
Vol 17 (12) ◽  
pp. 3015-3036 ◽  
Author(s):  
Yves Benoist ◽  
Toshiyuki Kobayashi
Keyword(s):  
Homogeneous Spaces ◽  
Reductive Homogeneous Spaces

scholarly journals Compactification of certain Clifford-Klein forms of reductive homogeneous spaces

2017 ◽  
Vol 66 (1) ◽  
pp. 49-84 ◽  
Author(s):  
François Guéritaud ◽  
Olivier Guichard ◽  
Fanny Kassel ◽  
Anna Wienhard
Keyword(s):  
Homogeneous Spaces ◽  
Reductive Homogeneous Spaces

scholarly journals A Note on Simple Anti-Commutative Algebras Obtained from Reductive Homogeneous Spaces

1968 ◽  
Vol 31 ◽  
pp. 105-124 ◽  
Author(s):  
Arthur A. Sagle
Keyword(s):  
Homogeneous Space ◽  
Lie Algebra ◽  
Lie Group ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Commutative Algebras ◽  
Direct Sum ◽  
Reductive Homogeneous Spaces ◽  
Connected Lie Group

LetGbe a connected Lie group andHa closed subgroup, then the homogeneous spaceM = G/His calledreductiveif there exists a decomposition(subspace direct sum) withwhereg(resp.) is the Lie algebra ofG(resp.H); in this case the pair (g,) is called areductive pair.

Classification of five-dimensional naturally reductive spaces

1985 ◽  
Vol 97 (3) ◽  
pp. 445-463 ◽  
Author(s):  
Oldřich Kowalski ◽  
Lieven Vanhecke
Keyword(s):  
General Theory ◽  
Symmetric Spaces ◽  
Homogeneous Spaces ◽  
Natural Generalization ◽  
Riemannian Symmetric Spaces ◽  
Reductive Homogeneous Spaces ◽  
Naturally Reductive ◽  
Volume Preserving ◽  
Number Of Authors

Naturally reductive homogeneous spaces have been studied by a number of authors as a natural generalization of Riemannian symmetric spaces. A general theory with many examples was well-developed by D'Atri and Ziller[3]. D'Atri and Nickerson have proved that all naturally reductive spaces are spaces with volume-preserving local geodesic symmetries (see [1] and [2]).

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