scholarly journals Codazzi Tensors and the Quasi-Statistical Structure Associated with Affine Connections on Three-Dimensional Lorentzian Lie Groups

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1459
Author(s):  
Tong Wu ◽  
Yong Wang
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Statistical Structure ◽  
Affine Connections ◽  
Codazzi Tensors

In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated with Bott connections, canonical connections and Kobayashi–Nomizu connections are Codazzi tensors associated with these connections. We also classify three-dimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott connections, canonical connections and Kobayashi–Nomizu connections.

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

scholarly journals Vacuum quantum effects on Lie groups with bi-invariant metrics

2019 ◽  
Vol 16 (08) ◽  
pp. 1950122
Author(s):  
A. I. Breev ◽  
A. V. Shapovalov
Keyword(s):  
Scalar Field ◽  
Lie Groups ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Particle Creation ◽  
Vacuum Expectation ◽  
Rotation Group ◽  
Momentum Tensor ◽  
Invariant Metrics ◽  
Field Equations

We consider the effects of vacuum polarization and particle creation of a scalar field on Lie groups with a non-stationary bi-invariant metric of the Robertson–Walker type. The vacuum expectation values of the energy momentum tensor for a scalar field determined by the group representation are found using the noncommutative integration method for the field equations instead of separation of variables. The results obtained are illustrated by the example of the three-dimensional rotation group.

scholarly journals PARALLEL SURFACES IN THREE-DIMENSIONAL LORENTZIAN LIE GROUPS

2010 ◽  
Vol 14 (1) ◽  
pp. 223-250 ◽  
Author(s):  
Giovanni Calvaruso ◽  
Joeri Van der Veken
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Parallel Surfaces
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