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 .

In this paper we study a large class of Weingarten surfaces which includes the constant mean curvature one surfaces and flat surfaces in the hyperbolic 3-space. We show that these surfaces can be parametrized by holomorphic data like minimal surfaces in the Euclidean 3-space and we use it to study their completeness. We also establish some existence and uniqueness theorems by studing the Platea...

We present a method for the precise determination of the volume of subsets of Rd which are bounded by a hypersurface parametrized by a set of refinable functions. The derivation is based on the linear refinement equations rather than on closed form expressions of these functions, which may not be available. In particular, our approach makes it possible to compute the area of planar domains boun...

For a two-dimensional surface M in the four-dimensional Euclidean space E we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and κ. The condition k = κ = 0 characterizes the surfaces consisting of flat points. The minimal surfaces are characterized by the equality κ − k = 0. The class of the surfaces with flat normal con...

To retrieve models from a data base for recognizing objects in stereo, a new formulation of patches of Dupin's Cyclide provides a succinct representation of surface shape. The parameters can be extracted from the Weingarten Map and its derivatives at a point where a contour meets an extremal boundary.

The Lagrangian star is a germ of the system ({L1, . . . , Lk}, p̃) of Lagrangian submanifolds in the symplectic manifold (M,ω). We investigate the symplectic group action on Lagrangian stars and construct the basic invariants of such action. The Kashiwara signature for 3-Lagrangian linear stars is generalized to the nonlinear case and the generalized contact classes for Lagrangian stars are cons...

This note is an extension of the paper [HMP]. The main theorem of [HMP] states that a relatively smooth hypersurface (i.e. a hypersurface whose singular locus has sufficient large codimension with respect to its degree) is unirational. A mild modification can generalize this to complete intersections. As an application, we will show the Fano variety of a relatively smooth hypersurface is also u...