TT-tensors and conformally flat structures on 3-manifolds

Details TT-tensors and conformally flat structures on 3-manifolds TT-tensors and conformally flat structures on 3-manifolds

1996-06-18

arxiv.org/abs/gr-qc/9606055v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages

Scientific paper

We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds $(M,g)$. The Cotton-York tensor linearized at $g$ maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. The question is answered affirmatively when $M$ is simply connected and has vanishing 2nd de Rham cohomology.

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