Shape representation as the intersection of n ? k hypersurfaces. Shape representation as the intersection of n ? k hypersurfaces. Abstract: We investigate the feasibility of representing implicitly a k-dimensional manifold embedded in the Euclidean space R n as the intersection of n ? k transverse hypersurfaces. From the analytical point of view, the embedded manifold is deened as the inverse i...

We consider Levi non-degenerate tube hypersurfaces in Cn+1 that are (k, n−k)-spherical, i.e., locally CR-equivalent to the hyperquadric with Levi form of the signature (k, n − k), with n ≤ 2k. We show that the number of affine equivalence classes of such hypersurfaces is infinite (in fact, uncountable) in the following cases: (i) k = n − 2, n ≥ 7; (ii) k = n − 3, n ≥ 7; (iii) k ≤ n − 4. For all...

Introduction We use results of Deligne on ...-adic monodromy and equidistribution, combined with elementary facts about the eigenvalues of elements in the orthogonal group, to give upper bounds for the average "middle Picard number" in various equicharacteristic families of even dimensional hypersurfaces, cf. 6.11, 6.12, 6.14, 7.6, 8.12. We also give upper bounds for the average MordellWeil ran...

In this article we explain how critical points of a perturbed Rabinowitz action functional give rise to leaf-wise intersection points in hypersurfaces of restricted contact type. This is used to derive existence results for hypersurfaces in general exact symplectic manifolds.

This paper is a continuation of our paper [HZ02] where we have built a combinatorial model for the torus fibrations of Calabi-Yau toric hypersurfaces. This part addresses the connection between the model torus fibration and the complex and Kähler geometry of the hypersurfaces.

The main purpose of this paper is to give fundamental properties of real lightlike hypersurfaces of paraquaternionic manifolds and to prove the non-existence of real lightlike hypersurfaces in paraquaternionic space form under some conditions. AMS MATHEMATICS SUBJECT CLASSIFICATION. Primary 53C15, Secondary 53C42, 53C50.

The problem of existence of spacelike hypersurfaces with constant mean curvature in asymptotically flat spacetimes is considered for a class of asymptotically Schwarzschild spacetimes satisfying an interior condition. Using a barrier construction, a proof is given of the existence of complete hypersurfaces with constant mean cuvature which intersect null infinity in a regular cut. 1991 Mathemat...

This paper introduces the notions of pseudo null curves in Minkowski 4-space. Meanwhile, some geometrical characterizations and the singularities of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces, which are generated by pseudo null curves, are considered in this paper. c ©2016 All rights reserved.

In this paper, we study locally strongly convex Tchebychev hypersurfaces, namely the {\it centroaffine totally umbilical hypersurfaces}, in $(n+1)$-dimensional affine space $\mathbb{R}^{n+1}$. We first make an ordinary-looking observation that such hypersurfaces are characterized by having a Riemannian structure admitting canonically defined closed conformal vector field. Then, taking advantage...