Isometry groups of three‐dimensional Lorentzian metrics

1994 ◽  
Vol 35 (2) ◽  
pp. 873-884 ◽  
Author(s):  
C. Bona ◽  
B. Coll
Keyword(s):  
Three Dimensional ◽  
Isometry Groups ◽  
Lorentzian Metrics

Certain homogeneous paracontact three-dimensional Lorentzian metrics

2017 ◽  
Vol 11 (01) ◽  
pp. 1850006
Author(s):  
Ali Haji-Badali ◽  
Elham Sourchi
Keyword(s):  
Vector Field ◽  
Three Dimensional ◽  
Einstein Manifolds ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Lorentzian Metrics

In this paper, we study three-dimensional homogeneous paracontact metric manifolds for which the Reeb vector field of the underlying paracontact structure satisfies a nullity condition. We give example of paraSasakian and non-paraSasakian [Formula: see text]-manifolds. Finally, we exhibit explicit example of [Formula: see text]-Einstein manifolds.

scholarly journals Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups

2017 ◽  
Vol 25 (2) ◽  
pp. 99-135
Author(s):  
Rory Biggs
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Isometry Group ◽  
Three Dimensional ◽  
Isotropy Subgroup ◽  
Left Translation ◽  
Isometry Groups ◽  
Group Automorphism ◽  
Group Of Automorphisms ◽  
Simply Connected

Abstract We investigate the isometry groups of the left-invariant Riemannian and sub-Riemannian structures on simply connected three-dimensional Lie groups. More specifically, we determine the isometry group for each normalized structure and hence characterize for exactly which structures (and groups) the isotropy subgroup of the identity is contained in the group of automorphisms of the Lie group. It turns out (in both the Riemannian and sub-Riemannian cases) that for most structures any isometry is the composition of a left translation and a Lie group automorphism.

Isometry groups of three‐dimensional Riemannian metrics

1992 ◽  
Vol 33 (1) ◽  
pp. 267-272 ◽  
Author(s):  
Carles Bona ◽  
Bartolomé Coll
Keyword(s):  
Three Dimensional ◽  
Riemannian Metrics ◽  
Isometry Groups
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