In our previous work (2002), we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse; in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semiRiemannian Banach space is an essen...

There exists a bijection between the configuration space of a linear pentapod and all points (u,v,w, px, py, pz)∈R located on the singular quadric Γ : u2+v2+w2 = 1, where (u,v,w) determines the orientation of the linear platform and (px, py, pz) its position. Then the set of all singular robot configurations is obtained by intersecting Γ with a cubic hypersurface Σ in R6, which is only quadrati...

In this article, we prove that there exists at least one chord orbit of Hamilton vector field connecting the Legendre submanifold on a given energy stable hypersurface in some symplectic manifolds. Démonstration de existence de chord orbital de hamiltonien en une stable hypersurface dans une variété symplectique. Résumé. Soit Σ une hypersurface close en variété symplectique, Il est de montrer q...

In this article, we prove that there exists at least one periodic orbit of Hamilton vector field on a given energy hypersurface in R2n which proves the longstanding Seifert’s conjecture. The more general results are also obtained. Démonstration de la Conjecture de Seifert sur existence de périodique orbital de hamiltonien en une hypersurface dans une variété symplectique. Résumé. Soit Σ une hyp...

Okumura gave a necessary and sufficient condition for an oriented real hypersurface of a Kähler manifold to be a contact metric manifold with respect to the naturally induced almost contact metric structure. In this paper, we discuss an oriented hypersurface of a quasi Kähler manifold and give a necessary and sufficient condition for such a hypersurface to be a quasi contact metric manifold wit...

We describe algorithmic methods for the Gauss-Manin connection of an isolated hypersurface singularity based on the microlocal structure of the Brieskorn lattice. They lead to algorithms for computing invariants like the monodromy, the spectrum, the spectral pairs, and M. Saito’s matrices A0 and A1. These algorithms use a normal form algorithm for the Brieskorn lattice, standard basis methods f...