We study 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.
@article{bwmeta1.element.bwnjournal-article-bcpv41z1p109bwm,
author = {Beig, R.},
title = {TT-tensors and conformally flat structures on 3-manifolds},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {109-118},
zbl = {0894.53044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z1p109bwm}
}
Beig, R. TT-tensors and conformally flat structures on 3-manifolds. Banach Center Publications, Tome 38 (1997) pp. 109-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z1p109bwm/
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