The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.

In this paper we study the hypersurfaces $M^n$ given as connected compact regular fibers of a differentiable map $f:{ℝ}^{n+1}\to ℝ$, in the cases in which $f$ has finitely many nondegenerate critical points in the unbounded component of ${ℝ}^{n+1}-M^n$.

Soit $\omega$ un germe en $0\in {\mathbf{C}}^n$ de 1-forme différentielle holomorphe, satisfaisant la condition d’intégrabilité $\omega \wedge d\omega =0$ et non dicritique, i.e. sur toute surface $Z$ non intégrale de $\omega$, on ne peut tracer, au voisinage de 0, qu’un nombre fini de germes de courbes analytiques $({\Gamma }_i,P_i)$, intégrales de $\omega$, avec $P_i\in Z\cap Sing\omega$. Alors $\omega$ possède un germe d’hypersurface analytique intégrale.