scholarly journals Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras

2015 ◽  
Author(s):  
Alexey A. Magazev ◽  
◽  
Vitaly V. Mikheyev ◽  
Igor V. Shirokov ◽  
◽  
...  
Keyword(s):  
Lie Algebras ◽  
Vector Fields ◽  
Invariant Vector ◽  
Structure Constants ◽  
Invariant Vector Fields

Harmonicity of vector fields on a class of Lorentzian solvable Lie groups

2018 ◽  
Vol 18 (3) ◽  
pp. 337-344 ◽  
Author(s):  
Ju Tan ◽  
Shaoqiang Deng
Keyword(s):  
Vector Field ◽  
Lie Groups ◽  
Lie Algebras ◽  
Critical Points ◽  
Vector Fields ◽  
Energy Functional ◽  
Smooth Vector ◽  
Solvable Lie Groups ◽  
Invariant Vector ◽  
Invariant Vector Fields

AbstractIn this paper, we consider a special class of solvable Lie groups such that for any x, y in their Lie algebras, [x, y] is a linear combination of x and y. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.

Semilinear PDEs in the Heisenberg group: The role of the right invariant vector fields

2010 ◽  
Vol 72 (2) ◽  
pp. 987-997 ◽  
Author(s):  
Isabeau Birindelli ◽  
Fausto Ferrari ◽  
Enrico Valdinoci
Keyword(s):  
Heisenberg Group ◽  
Vector Fields ◽  
Invariant Vector ◽  
Semilinear Pdes ◽  
The Right ◽  
Invariant Vector Fields

Motions of Curves in 4-Dimensional Galilean Space G4

2021 ◽  
pp. 2150153
Author(s):  
Hülya Gün Bozok ◽  
Sezin Aykurt Sepet ◽  
Mahmut Ergüt
Keyword(s):  
Vector Fields ◽  
Invariant Vector ◽  
Burgers Equations ◽  
Frenet Equations ◽  
Inextensible Flows ◽  
Galilean Space ◽  
Invariant Vector Fields

In this paper, we investigate the flow of curve and its equiform geometry in 4-dimensional Galilean space. We obtain that the Frenet equations and curvatures of inextensible flows of curves and its equiformly invariant vector fields and intrinsic quantities are independent of time. We find that the motions of curves and its equiform geometry can be defined by the inviscid and stochastic Burgers’ equations in 4-dimensional Galilean space.

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