Regular projectively Anosov flows with compact leaves

Takeo Noda[1]

  • [1] University of Tokyo, Graduate School of Mathematical Sciences, 3-8-1 Komaba, Meguro-Ku, Tokyo 153-8914 (Japon)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 2, page 481-497
  • ISSN: 0373-0956

Abstract

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This paper concerns projectively Anosov flows φ t with smooth stable and unstable foliations ℱ s and ℱ u on a Seifert manifold M . We show that if the foliation ℱ s or ℱ u contains a compact leaf, then the flow φ t is decomposed into a finite union of models which are defined on T 2 × I and bounded by compact leaves, and therefore the manifold M is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible tori.

How to cite

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Noda, Takeo. "Regular projectively Anosov flows with compact leaves." Annales de l’institut Fourier 54.2 (2004): 481-497. <http://eudml.org/doc/116119>.

@article{Noda2004,
abstract = {This paper concerns projectively Anosov flows $\phi ^t$ with smooth stable and unstable foliations $\{\mathcal \{F\}\}^s$ and $\{\mathcal \{F\}\}^u$ on a Seifert manifold $M$. We show that if the foliation $\{\mathcal \{F\}\}^s$ or $\{\mathcal \{F\}\}^u$ contains a compact leaf, then the flow $\phi ^t$ is decomposed into a finite union of models which are defined on $\{T^2\} \times I$ and bounded by compact leaves, and therefore the manifold $M$ is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible tori.},
affiliation = {University of Tokyo, Graduate School of Mathematical Sciences, 3-8-1 Komaba, Meguro-Ku, Tokyo 153-8914 (Japon)},
author = {Noda, Takeo},
journal = {Annales de l’institut Fourier},
keywords = {projectively Anosov flows; stable foliations; bi-contact structures; Anosov foliation; regular projectively Anosov flow; stable foliation; compact leaf; Seifert manifold; bi-contact structure},
language = {eng},
number = {2},
pages = {481-497},
publisher = {Association des Annales de l'Institut Fourier},
title = {Regular projectively Anosov flows with compact leaves},
url = {http://eudml.org/doc/116119},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Noda, Takeo
TI - Regular projectively Anosov flows with compact leaves
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 2
SP - 481
EP - 497
AB - This paper concerns projectively Anosov flows $\phi ^t$ with smooth stable and unstable foliations ${\mathcal {F}}^s$ and ${\mathcal {F}}^u$ on a Seifert manifold $M$. We show that if the foliation ${\mathcal {F}}^s$ or ${\mathcal {F}}^u$ contains a compact leaf, then the flow $\phi ^t$ is decomposed into a finite union of models which are defined on ${T^2} \times I$ and bounded by compact leaves, and therefore the manifold $M$ is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible tori.
LA - eng
KW - projectively Anosov flows; stable foliations; bi-contact structures; Anosov foliation; regular projectively Anosov flow; stable foliation; compact leaf; Seifert manifold; bi-contact structure
UR - http://eudml.org/doc/116119
ER -

References

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