Lie groups and homogeneous manifolds

2004 ◽  
pp. 269-332
Author(s):  
A. Kirillov
Keyword(s):  
Lie Groups ◽  
Homogeneous Manifolds

Naturally reductive homogeneous (α,β) spaces

2020 ◽  
Vol 17 (08) ◽  
pp. 2050117
Author(s):  
Parisa Bahmandoust ◽  
Dariush Latifi
Keyword(s):  
Lie Groups ◽  
Explicit Formula ◽  
Flag Curvature ◽  
Homogeneous Manifolds ◽  
Randers Metrics ◽  
Naturally Reductive ◽  
Special Case

In this paper, we study naturally reductive [Formula: see text]-metrics on homogeneous manifolds. We show that naturally reductive [Formula: see text]-metrics arise only when [Formula: see text] is naturally reductive and some conditions on [Formula: see text] is satisfied. We give an explicit formula for the flag curvature of naturally reductive [Formula: see text]metrics which improves the flag curvature formula of naturally reductive Randers metrics given in [D. Latifi, Naturally reductive homogeneous Randers spaces, J. Geom. Phys. 60 (2010) 1968–1973]. As a special case, we give an explicit formula for the flag curvature of bi-invariant [Formula: see text]-metrics on Lie groups.

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