2017/11/03 by Carlos Batista, Batista, Carlos
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #gr-qc #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.1711.01337
13 pages
arxiv created 2017/11/03 · arxiv updated 2017/11/07
It is natural to expect and simple to prove that every conformally flat space possess the maximal number of conformal Killing vector fields (CKVs). On the other hand, it is interesting to ask whether the converse is true. Is conformal flatness a necessary condition for the existence of the maximal number of CKVs? In this review article it is proven that the answer is yes, a space admits the maximal number of CKVs if, and only if, it is conformally flat.