Translation foliations of codimension one on compact affine manifolds

Turiel, Francisco

Banach Center Publications, Tome 38 (1997), p. 171-182 / Harvested from The Polish Digital Mathematics Library

Résumé

Consider two foliations $ℱ_{1}$ and $ℱ_{2}$ , of dimension one and codimension one respectively, on a compact connected affine manifold $(M, \nabla)$ . Suppose that $\nabla_{T ℱ_{1}} T ℱ_{2} \subset T ℱ_{2}$ ; $\nabla_{T ℱ_{2}} T ℱ_{1} \subset T ℱ_{1}$ and $T M = T ℱ_{1} \oplus T ℱ_{2}$ . In this paper we show that either $ℱ_{2}$ is given by a fibration over $S^{1}$ , and then $ℱ_{1}$ has a great degree of freedom, or the trace of $ℱ_{1}$ is given by a few number of types of curves which are completely described. Moreover we prove that $ℱ_{2}$ has a transverse affine structure.

Publié le : 1997-01-01

Zbl 0897.53023

EUDML-ID : urn:eudml:doc:208660

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     author = {Turiel, Francisco},
     title = {Translation foliations of codimension one on compact affine manifolds},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {171-182},
     zbl = {0897.53023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p171bwm}
}

Turiel, Francisco. Translation foliations of codimension one on compact affine manifolds. Banach Center Publications, Tome 38 (1997) pp. 171-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p171bwm/

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