Abstract
In a recent paper, Carot et al considered carefully the definition ofcylindrical symmetry as a specialization of the case of axial symmetry.One of their propositions states that if there is a secondKilling vector, which together with the one generating theaxial symmetry, forms the basis of a two-dimensional Lie algebra, thenthe two Killing vectors must commute, thus generating an Abelian group.In this comment a similar result, valid under considerably weakerassumptions, is recalled: any two-dimensional Lie transformation groupwhich contains a one-dimensional subgroup whose orbits are circles,must be Abelian. The method used to prove this result is extended to apply tothree-dimensional Lie transformation groups. It is shown that theexistence of a one-dimensional subgroup with closed orbits restricts the Bianchitype of the associated Lie algebra to be I (Abelian), II,III, VIIq = 0, VIII or IX. The relationship between the present approach and that ofthe original paper is discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
