2004/08/17 by Mario Listing, Listing, Mario
Mathematics · #53A30 #53A55 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A30 #msc:53A55
paper · pdf · doi:10.48550/arxiv.math/0408224
13 pages
arxiv created 2004/08/17 · arxiv updated 2009/12/01
This paper presents conformal invariants for Riemannian manifolds of dimension greater than or equal to four whose vanishing is necessary for a Riemannian manifold to be conformally related to an Einstein space. One of the invariants is a modification of the Cotton tensor, the other is a n--dimensional version of the Bach tensor. In general both tensors are smooth only on an open and dense subset of M, but this subset is invariant under conformal transformations. Moreover, we generalize the main result of "Conformal Einstein Spaces in N--Dimensions" published in Ann. Global Anal. Geom. \bf 20(2) (2001).