scholarly journals On the Sectional Curvature Operator of Three-Dimensional Lie Groups with Left-Invariant Lorentzian Metrics

2017 ◽  
Vol 1 ◽  
Author(s):  
S.V. Klepikova ◽  
◽  
O.P. Khromova ◽  
Keyword(s):  
Sectional Curvature ◽  
Lie Groups ◽  
Three Dimensional ◽  
Curvature Operator ◽  
Lorentzian Metrics

scholarly journals ON THE RANDERS METRICS ON TWO-STEP HOMOGENEOUS NILMANIFOLDS OF DIMENSION FIVE

2011 ◽  
Vol 08 (03) ◽  
pp. 501-510 ◽  
Author(s):  
HAMID REZA SALIMI MOGHADDAM
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Lie Groups ◽  
Three Dimensional ◽  
Flag Curvature ◽  
Nilpotent Lie Groups ◽  
Randers Metric ◽  
Levi Civita Connection ◽  
Simply Connected ◽  
Randers Metrics

In this paper we study the geometry of simply connected two-step nilpotent Lie groups of dimension five. We give the Levi–Civita connection, curvature tensor, sectional and scalar curvatures of these spaces and show that they have constant negative scalar curvature. Also we show that the only space which admits left-invariant Randers metric of Berwald type has three-dimensional center. In this case the explicit formula for computing flag curvature is obtained and it is shown that flag curvature and sectional curvature have the same sign.

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 Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 246
Author(s):  
Yan Zhao ◽  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Three Dimensional ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Ricci Operator ◽  
Cosymplectic Manifold

Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds.

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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