TT-tensors and conformally flat structures on 3-manifolds
Volume 41 / 1997
Banach Center Publications 41 (1997), 109-118
DOI: 10.4064/-41-1-109-118
Abstract
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.
