scholarly journals Natural and conjugate mates of Frenet curves in three-dimensional Lie group

2021 ◽  
Vol 70 (1) ◽  
pp. 522-540
Author(s):  
Mahmut MAK
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Frenet Curves

scholarly journals Associated Curves of Frenet curves in Three Dimensional Compact Lie Group

2015 ◽  
Vol 16 (2) ◽  
pp. 953-964 ◽  
Author(s):  
Sezai Kızıltuğ ◽  
Mehmet Önder
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Compact Lie Group ◽  
Frenet Curves

scholarly journals The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group

2014 ◽  
Vol 195 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Adriana A. Cintra ◽  
Francesco Mercuri ◽  
Irene I. Onnis
Keyword(s):  
Lie Group ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Björling Problem

scholarly journals On the Björling problem in a three-dimensional Lie group

2009 ◽  
Vol 53 (2) ◽  
pp. 431-440 ◽  
Author(s):  
Francesco Mercuri ◽  
Irene I. Onnis
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Björling Problem

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.

∗-Ricci tensor on almost Kenmotsu 3-manifolds

2020 ◽  
Vol 17 (13) ◽  
pp. 2050196
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Lie Group ◽  
Ricci Tensor ◽  
Three Dimensional ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Addition Formula ◽  
Kenmotsu Manifold ◽  
Ricci Operator ◽  
Necessary And Sufficient ◽  
Parallel Ricci Tensor

In this paper, we obtain the expressions of the ∗-Ricci operator of a three-dimensional almost Kenmotsu manifold [Formula: see text] and find that the ∗-Ricci tensor is not symmetric for [Formula: see text]. We obtain a necessary and sufficient condition for the ∗-Ricci tensor to be symmetric and proved that if the ∗-Ricci tensor of a non-Kenmotsu almost Kenmotsu 3-[Formula: see text]-manifold [Formula: see text] is symmetric, then [Formula: see text] is locally isometric to a three-dimensional non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure. Further, it is shown that the ∗-Ricci tensor of a non-Kenmotsu almost Kenmotsu 3-manifold [Formula: see text] is parallel if and only if [Formula: see text] is ∗-Ricci flat. In addition, [Formula: see text] satisfying [Formula: see text] is locally isometric to [Formula: see text]. Finally, we discuss about [Formula: see text]-parallel ∗-Ricci tensor on almost Kenmotsu 3-manifolds.

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