On the Signature of Ricci Curvature Tensor Operator of Three-Dimensional Lie Groups with Left-Invariant Lorentzian Metrics

2015 ◽  
Author(s):  
Svetlana Pastukhova ◽  
◽  
Olesya Khromova ◽  
Keyword(s):  
Lie Groups ◽  
Ricci Curvature ◽  
Curvature Tensor ◽  
Three Dimensional ◽  
Tensor Operator ◽  
Lorentzian Metrics

scholarly journals Sectional and Ricci Curvature for Three-Dimensional Lie Groups

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Gerard Thompson ◽  
Giriraj Bhattarai
Keyword(s):  
Automorphism Group ◽  
Lie Groups ◽  
Ricci Curvature ◽  
Lie Group ◽  
Systematic Study ◽  
Three Dimensional ◽  
Invariant Metrics ◽  
Curvature Function ◽  
Invariant Metric ◽  
Curvature Tensors

Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.

Invariant Ricci solitons on three-dimensional metric Lie groups with semi-symmetric connection

2021 ◽  
pp. 80-85
Author(s):  
Pavel Nikolaevich Klepikov ◽  
◽  
Evgeny Dmitrievich Rodionov ◽  
Olesya Pavlovna Khromova ◽  
◽  
...  
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Ricci Solitons ◽  
Symmetric Connection

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 On Mannheim partner curves in three dimensional Lie groups

2014 ◽  
Vol 15 (2) ◽  
pp. 467 ◽  
Author(s):  
Ismail Gök ◽  
O. Zeki Okuyucu ◽  
Nejat Ekmekci ◽  
Yusuf Yayli
Keyword(s):  
Lie Groups ◽  
Three Dimensional

scholarly journals $$\hbox {K}_{1}$$ K 1 -congruences for three-dimensional Lie groups

2018 ◽  
Vol 43 (1) ◽  
pp. 161-211 ◽  
Author(s):  
Daniel Delbourgo ◽  
Qin Chao
Keyword(s):  
Lie Groups ◽  
Three Dimensional

scholarly journals On local isometric embeddings of three-dimensional Lie groups

2019 ◽  
Vol 205 (1) ◽  
pp. 191-219
Author(s):  
Yoshio Agaoka ◽  
Takahiro Hashinaga
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Isometric Embeddings
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