The Open Mathematics Journal
2011, 4 : 5-11Published online 2011 December 28. DOI: 10.2174/1874117701104010005
Publisher ID: TOMATJ-4-5
The Lie Algebra of Local Killing Fields
Department of Mathematics, Trinity Western University, 7600 Glover Road, Langley, BC, V2Y 1Y1
Canada.
ABSTRACT
We present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fields about a given point on the manifold. As an application, we provide a local classification of the types of surfaces that admit the various possible Lie algebras of local Killing fields, in terms of the Gaussian curvature.