York decompositions for the Codazzi, Killing and Ricci tensors
Abstract
The York decomposition of the space of symmetric two-tensors originated in theoretical physics and has found applications in Riemannian geometry, as illustrated by its use in Besse’s famous monograph on Einstein manifolds. In this paper, we derive York decompositions for Codazzi, Killing and Rucci tensors on a closed Riemannian manifold. In particular, we derive the York decompositions for the Codazzi, Killing and Ricci tensors with constant trace.
Reference
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