We generalize Griffiths’ theorem on the Hodge filtration of the primitive cohomology of a smooth projective hypersurface, using the local Bernstein-Sato polynomials, the V -filtration of Kashiwara and Malgrange along the hypersurface and the Brieskorn module of the global defining equation of the hypersurface.

In this paper, we study the close spacelike hypersurfaces in de Sitter space. Using Bonnet-Myer’s theorem, we prove a rigidity theorem for spacelike hypersurfaces without the constancy condition on the mean curvature or the scalar curvature. M.S.C. 2010: 53C40, 53B30.

The main purpose of this paper is to study biharmonic hypersurface in a quasi-paraSasakian manifold $\mathbb{Q}^{2m+1}$. Biharmonic hypersurfaces are special cases maps and the critical points bienergy functional. condition biharmonicity for non-degenerate $\mathbb{Q}^{2m+1}$ investigated both cases: either characteristic vector field unit normal or it belongs tangent space hypersurface. Some r...

Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface, and also define a functor to the stable module category of maximal Cohen-Macaulay modules on the hypersurface. We introduce a new functorial concept of matrix factorizations for complete intersections that allows us to describe the asymptotic structure of mi...

D.E . BARRETT AND J . E . FORNAESS We study the regularity of the induced foliation of a Levi-flat hypersurface in C'° , showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question .

0. Introduction and Preliminary 2 0.1. Existence and uniqueness theorem 2 0.2. Equation of a chain 7 1. Nonsingular matrices 9 1.1. A family of nonsingular matrices 9 1.2. Sufficient condition for Nonsingularity 12 1.3. Estimates 16 2. Local automorphism group of a real hypersurface 23 2.1. Polynomial Identities 23 2.2. Injectivity of a Linear Mapping 33 2.3. Beloshapka-Loboda Theorem 42 3. Com...