Ball-homogeneous and disk-homogeneous Riemannian manifolds

1982 ◽  
Vol 180 (4) ◽  
pp. 429-444 ◽  
Author(s):  
Old?ich Kowalski ◽  
Lieven Vanhecke
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

scholarly journals Cyclic homogeneous Riemannian manifolds

2015 ◽  
Vol 195 (5) ◽  
pp. 1619-1637 ◽  
Author(s):  
P. M. Gadea ◽  
J. C. González-Dávila ◽  
J. A. Oubiña
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

On δ-homogeneous Riemannian manifolds. II

2009 ◽  
Vol 50 (2) ◽  
pp. 214-222 ◽  
Author(s):  
V. N. Berestovskiĭ ◽  
Yu. G. Nikonorov
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

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.

scholarly journals Compact homogeneous Riemannian manifolds with low coindex of symmetry

2017 ◽  
Vol 19 (1) ◽  
pp. 221-254 ◽  
Author(s):  
Jürgen Berndt ◽  
Carlos Olmos ◽  
Silvio Reggiani
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds
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