Classification of 3-dimensional left-invariant almost paracontact metric structures

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Complete Classification ◽  
Natural Assumption ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

scholarly journals Lie groups as 3-dimensional almost contact B-metric manifolds

2014 ◽  
Vol 106 (2) ◽  
pp. 229-242 ◽  
Author(s):  
Hristo Manev ◽  
Dimitar Mekerov
Keyword(s):  
Lie Groups ◽  
3 Dimensional

scholarly journals The index of symmetry of three-dimensional Lie groups with a left-invariant metric

2018 ◽  
Vol 18 (4) ◽  
pp. 395-404 ◽  
Author(s):  
Silvio Reggiani
Keyword(s):  
Lie Groups ◽  
Constant Curvature ◽  
Lie Group ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Invariant Metric ◽  
3 Dimensional ◽  
Space Of Constant Curvature ◽  
Positive Index

Abstract We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry, and we explain in what cases the group fibers over a 2-dimensional space of constant curvature.

scholarly journals Seifert invariants of left-quotients of 3-dimensional simple Lie groups

1995 ◽  
Vol 66 (2) ◽  
pp. 117-127 ◽  
Author(s):  
Hansjörg Geiges ◽  
Jesús Gonzalo
Keyword(s):  
Lie Groups ◽  
3 Dimensional ◽  
Simple Lie Groups

Grassmann geometry on the 3-dimensional non-unimodular Lie groups

2019 ◽  
Vol 48 (2) ◽  
pp. 385-406
Author(s):  
Jun-ichi INOGUCHI ◽  
Hiroo NAITOH
Keyword(s):  
Lie Groups ◽  
3 Dimensional ◽  
Grassmann Geometry
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