scholarly journals Classification of compact homogeneous spaces with invariant symplectic structures

1997 ◽  
Vol 3 (7) ◽  
pp. 52-54
Author(s):  
Daniel Guan
Keyword(s):  
Homogeneous Spaces ◽  
Symplectic Structures

Classification of invariant Einstein metrics on certain compact homogeneous spaces

2019 ◽  
Vol 63 (4) ◽  
pp. 755-776
Author(s):  
Zaili Yan ◽  
Huibin Chen ◽  
Shaoqiang Deng
Keyword(s):  
Einstein Metrics ◽  
Homogeneous Spaces

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]).

scholarly journals A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ1= ρ2≠ ρ3

1993 ◽  
Vol 132 ◽  
pp. 1-36 ◽  
Author(s):  
Oldřich Kowalski
Keyword(s):  
Differential Geometry ◽  
Homogeneous Spaces ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Main Motivation ◽  
Locally Homogeneous ◽  
Riemannian Spaces

This paper has been motivated by various problems and results in differential geometry. The main motivation is the study of curvature homogeneous Riemannian spaces initiated in 1960 by I.M. Singer (see Section 9—Appendix for the precise definitions and references). Up to recently, only sporadic classes of examples have been known of curvature homogeneous spaces which are not locally homogeneous. For instance, isoparametric hypersurfaces in space forms give nice examples of nontrivial curvature homogeneous spaces (see [FKM]). To study the topography of curvature homogeneous spaces more systematically, it is natural to start with the dimension n = 3. The following results and problems have been particularly inspiring.

scholarly journals On a classification of fat bundles over compact homogeneous spaces

2016 ◽  
Vol 49 ◽  
pp. 131-141
Author(s):  
Maciej Bocheński ◽  
Anna Szczepkowska ◽  
Aleksy Tralle ◽  
Artur Woike
Keyword(s):  
Homogeneous Spaces
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