# Translation foliations of codimension one on compact affine manifolds

Banach Center Publications (1997)

- Volume: 39, Issue: 1, page 171-182
- ISSN: 0137-6934

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topTuriel, Francisco. "Translation foliations of codimension one on compact affine manifolds." Banach Center Publications 39.1 (1997): 171-182. <http://eudml.org/doc/208660>.

@article{Turiel1997,

abstract = {Consider two foliations $\{\mathcal \{F\}\}_1$ and $\{\mathcal \{F\}\}_2$, of dimension one and codimension one respectively, on a compact connected affine manifold $(M,\nabla )$. Suppose that $\nabla _\{T\{\mathcal \{F\}\}_1\} T\{\mathcal \{F\}\}_2\subset T\{\mathcal \{F\}\}_2$; $\nabla _\{T\{\mathcal \{F\}\}_2\} T\{\mathcal \{F\}\}_1\subset T\{\mathcal \{F\}\}_1$ and $TM = T\{\mathcal \{F\}\}_1\oplus T\{\mathcal \{F\}\}_2$. In this paper we show that either $\{\mathcal \{F\}\}_2$ is given by a fibration over $S^1$, and then $\{\mathcal \{F\}\}_1$ has a great degree of freedom, or the trace of $\{\mathcal \{F\}\}_1$ is given by a few number of types of curves which are completely described. Moreover we prove that $\{\mathcal \{F\}\}_2$ has a transverse affine structure.},

author = {Turiel, Francisco},

journal = {Banach Center Publications},

keywords = {translation foliations; transverse affine structure},

language = {eng},

number = {1},

pages = {171-182},

title = {Translation foliations of codimension one on compact affine manifolds},

url = {http://eudml.org/doc/208660},

volume = {39},

year = {1997},

}

TY - JOUR

AU - Turiel, Francisco

TI - Translation foliations of codimension one on compact affine manifolds

JO - Banach Center Publications

PY - 1997

VL - 39

IS - 1

SP - 171

EP - 182

AB - Consider two foliations ${\mathcal {F}}_1$ and ${\mathcal {F}}_2$, of dimension one and codimension one respectively, on a compact connected affine manifold $(M,\nabla )$. Suppose that $\nabla _{T{\mathcal {F}}_1} T{\mathcal {F}}_2\subset T{\mathcal {F}}_2$; $\nabla _{T{\mathcal {F}}_2} T{\mathcal {F}}_1\subset T{\mathcal {F}}_1$ and $TM = T{\mathcal {F}}_1\oplus T{\mathcal {F}}_2$. In this paper we show that either ${\mathcal {F}}_2$ is given by a fibration over $S^1$, and then ${\mathcal {F}}_1$ has a great degree of freedom, or the trace of ${\mathcal {F}}_1$ is given by a few number of types of curves which are completely described. Moreover we prove that ${\mathcal {F}}_2$ has a transverse affine structure.

LA - eng

KW - translation foliations; transverse affine structure

UR - http://eudml.org/doc/208660

ER -

## References

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