Conformally invariant Cotton and Bach tensor in N-dimensions

Details Conformally invariant Cotton and Bach tensor in N-dimensions Conformally invariant Cotton and Bach tensor in N-dimensions

2004-08-17

arxiv.org/abs/math/0408224v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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 \emph{Ann. Global Anal. Geom.} {\bf 20}(2) (2001).

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