TT-tensors and conformally flat structures on 3-manifolds

R. Beig

Banach Center Publications (1997)

  • Volume: 41, Issue: 1, page 109-118
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Beig, R.. "TT-tensors and conformally flat structures on 3-manifolds." Banach Center Publications 41.1 (1997): 109-118. <http://eudml.org/doc/252202>.

@article{Beig1997,
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.},
author = {Beig, R.},
journal = {Banach Center Publications},
keywords = {TT-tensors; essential infinitesimal deformations; conformally flat 3-manifolds; Cotton-York tensor},
language = {eng},
number = {1},
pages = {109-118},
title = {TT-tensors and conformally flat structures on 3-manifolds},
url = {http://eudml.org/doc/252202},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Beig, R.
TI - TT-tensors and conformally flat structures on 3-manifolds
JO - Banach Center Publications
PY - 1997
VL - 41
IS - 1
SP - 109
EP - 118
AB - 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.
LA - eng
KW - TT-tensors; essential infinitesimal deformations; conformally flat 3-manifolds; Cotton-York tensor
UR - http://eudml.org/doc/252202
ER -

References

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