arXiv subjects

Aziz El Kacimi Alaoui

Publications and source records attributed to Aziz El Kacimi Alaoui.

3 recordsLinked to original sources

arXiv2019

Cohomologie feuilletée du flot affine de Reeb sur la variété de Hopf ${\Bbb S}^n\times {\Bbb S}^1$

We determine explicitly the foliated cohomology $H_{\cal F}^\ast (M)$ of the affine Reeb flow ${\cal F}$ on the Hopf manifold ${\Bbb S}^n\times {\Bbb S}^1$. The vector space $H_{\cal F}^1(M)$ contains exactly the obstructions to solve the cohomological equation $X\cdot f=g$ where $f$ and $g$ are $C^\infty $-functions and $X$ is any non singular vector field defining the foliation ${\cal F}$. The topological dual of $H_{\cal F}^1(M)$ is the space of distributions invariant by $X$.

math.DG↗

arXiv2019

Cohomologie de Dolbeault feuilletée du feuilletage complexe affine de Reeb

Let ${\cal F}$ be a complex affine Reeb foliation of dimension $1$ on the Hopf manifold ${\Bbb S}^{n+1}\times {\Bbb S}^1$. We prove that its foliated Dolbeault cohomology in degree $1$ is isomorphic to ${\Bbb C}$ by giving an explicit generator.

math.CV↗

arXiv2019

Area and perimeter foliations on spaces of polygons

We describe all families of star-shaped n-polygons in the Euclidean plane with prescribed perimeter and area ; they are leaves of a foliation F on the space of star-shaped n-polygons. By the way, we study some geometric properties of convex polygons, for instance their inscriptibility in a circle and their regularity in relation with the perimeter and the area.

math.DG↗