- Tytuł:
- Translation foliations of codimension one on compact affine manifolds
- Autorzy:
- Turiel, Francisco
- Powiązania:
- https://bibliotekanauki.pl/articles/1358542.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Consider two foliations ${\cal F}_1$ and ${\cal F}_2$, of dimension one and codimension one respectively, on a compact connected affine manifold $(M,\nabla)$. Suppose that $\nabla_{T{\cal F}_1} T{\cal F}_2\subset T{\cal F}_2$; $\nabla_{T{\cal F}_2} T{\cal F}_1\subset T{\cal F}_1$ and $TM = T{\cal F}_1\oplus T{\cal F}_2$. In this paper we show that either ${\cal F}_2$ is given by a fibration over $S^1$, and then ${\cal F}_1$ has a great degree of freedom, or the trace of ${\cal F}_1$ is given by a few number of types of curves which are completely described. Moreover we prove that ${\cal F}_2$ has a transverse affine structure.
- Źródło:
-
Banach Center Publications; 1997, 39, 1; 171-182
0137-6934 - Pojawia się w:
- Banach Center Publications
- Dostawca treści:
- Biblioteka Nauki
Artykuł