A criterion for the existence of Killing vectors in 3D. (18th July 2018)

• Record Type: Journal Article
• Authors: Kruglikov, Boris; Tomoda, Kentaro
• Is Part Of: Classical and quantum gravity. Volume 35:Number 16(2018:Aug.)
• Publication Date: 2018-07-18
• Subjects: Killing vector -- isometry group -- curvature invariant -- Cartan–Karlhede algorithm; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/aad11d
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: A three-dimensional Riemannian manifold has locally 6, 4, 3, 2, 1 or no independent Killing vectors. We present an explicit algorithm for the computing dimension of infinitesimal isometry algebra. It branches according to the values of curvature invariants. These are relative differential invariants computed via curvature, but they are not scalar polynomial Weyl invariants. We compare our obstructions to the existence of Killing vectors with the known existence criteria due to Singer, Kerr and others.