- Definition
- See also
- References
Codazzi tensors (named after Delfino Codazzi) arise very naturally in the study of Riemannian manifolds with harmonic curvature or harmonic Weyl tensor. In fact, existence of Codazzi tensors impose strict conditions on the curvature tensor of the manifold.
Definition
Let 
be a n-dimensional Riemannian manifold for 
, let 
be a tensor, and let 
be a Levi-Civita connection on the manifold. We say that the tensor is a Codazzi Tensor if 
.
See also
- Weyl–Schouten theorem
References
- Arthur Besse, Einstein Manifolds, Springer (1987).
1 : Tensors
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