Projectively Anosov flows with differentiable (un)stable foliations

Takeo Noda

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 5, page 1617-1647
  • ISSN: 0373-0956

Abstract

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We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on T 2 which can be extended on a neighbourhood of T 2 into a projectively Anosov flow so that T 2 is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on T 3 . In this case, the only flows on T 2 which extend to T 3 (in the above way) are the linear flows.

How to cite

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Noda, Takeo. "Projectively Anosov flows with differentiable (un)stable foliations." Annales de l'institut Fourier 50.5 (2000): 1617-1647. <http://eudml.org/doc/75466>.

@article{Noda2000,
abstract = {We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on $T^2$ which can be extended on a neighbourhood of $T^2$ into a projectively Anosov flow so that $T^2$ is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on $T^3$. In this case, the only flows on $T^2$ which extend to $T^3$ (in the above way) are the linear flows.},
author = {Noda, Takeo},
journal = {Annales de l'institut Fourier},
keywords = {projectively Anosov flows; stable foliations; bi-contact structures},
language = {eng},
number = {5},
pages = {1617-1647},
publisher = {Association des Annales de l'Institut Fourier},
title = {Projectively Anosov flows with differentiable (un)stable foliations},
url = {http://eudml.org/doc/75466},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Noda, Takeo
TI - Projectively Anosov flows with differentiable (un)stable foliations
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 5
SP - 1617
EP - 1647
AB - We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on $T^2$ which can be extended on a neighbourhood of $T^2$ into a projectively Anosov flow so that $T^2$ is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on $T^3$. In this case, the only flows on $T^2$ which extend to $T^3$ (in the above way) are the linear flows.
LA - eng
KW - projectively Anosov flows; stable foliations; bi-contact structures
UR - http://eudml.org/doc/75466
ER -

References

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