scholarly journals Geodesic orbit and naturally reductive nilmanifolds associated with graphs

2020 ◽  
Vol 293 (4) ◽  
pp. 754-760
Author(s):  
Y. Nikolayevsky
Keyword(s):  
Naturally Reductive

scholarly journals The Classification of 7- and 8-dimensional Naturally Reductive Spaces

2019 ◽  
Vol 72 (5) ◽  
pp. 1246-1274 ◽  
Author(s):  
Reinier Storm
Keyword(s):  
New Method ◽  
Structure Theory ◽  
New Construction ◽  
Naturally Reductive

AbstractA new method for classifying naturally reductive spaces is presented. This method relies on a new construction and the structure theory of naturally reductive spaces recently developed by the author. This method is applied to obtain the classification of all naturally reductive spaces in dimension 7 and 8.

Naturally Reductive Homogeneous Riemannian Manifolds

1985 ◽  
Vol 37 (3) ◽  
pp. 467-487 ◽  
Author(s):  
Carolyn S. Gordon
Keyword(s):  
Homogeneous Space ◽  
Lie Group ◽  
Riemannian Manifolds ◽  
Homogeneous Spaces ◽  
Invariant Metrics ◽  
List Type ◽  
Left Invariant Metrics ◽  
Homogeneous Riemannian Manifolds ◽  
Transitive Subgroup ◽  
Naturally Reductive

The simple algebraic and geometric properties of naturally reductive metrics make them useful as examples in the study of homogeneous Riemannian manifolds. (See for example [2], [3], [15]). The existence and abundance of naturally reductive left-invariant metrics on a Lie group G or homogeneous space G/L reflect the structure of G itself. Such metrics abound on compact groups, exist but are more restricted on noncompact semisimple groups, and are relatively rare on solvable groups. The goals of this paper are(i) to study all naturally reductive homogeneous spaces of G when G is either semisimple of noncompact type or nilpotent and(ii) to give necessary conditions on a Riemannian homogeneous space of an arbitrary Lie group G in order that the metric be naturally reductive with respect to some transitive subgroup of G.

Three-Dimensional Naturally Reductive Homogeneous Lorentzian Manifolds

2008 ◽  
Vol 5 (1) ◽  
pp. 113-131 ◽  
Author(s):  
Nadjia Haouari ◽  
Wafaa Batat ◽  
Noureddine Rahmani ◽  
Salima Rahmani
Keyword(s):  
Three Dimensional ◽  
Lorentzian Manifolds ◽  
Naturally Reductive

scholarly journals The index of symmetry of compact naturally reductive spaces

2014 ◽  
Vol 277 (3-4) ◽  
pp. 611-628 ◽  
Author(s):  
Carlos Olmos ◽  
Silvio Reggiani ◽  
Hiroshi Tamaru
Keyword(s):  
Naturally Reductive
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