We obtain a classification of codimension one holomorphic foliations on P with degenerate Gauss maps.

In this paper we introduce the fourth fundamental form for the hypersurfaces in H and the space-like hypersurfaces in S 1 and discuss the conformality of the normal Gauss maps of the hypersurfaces in H and S 1 . Particularly, we discuss the surfaces with conformal normal Gauss maps in H and S 1 and prove a duality property. We give the Weierstrass representation formula for the space-like surfa...

We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As applications, we prove a Bernstein theorem which says that if the image of the Gauss map is bounded from one side, then the spacelike constant mean curvature hypersurface must be linear. This result extends the previous theorems obtained...

We give an estimate of the Gauss curvature for minimal surfaces in R m whose Gauss map omits more than m(m + 1)=2 hyperplanes in P m?1 (C).

A classical theorem in complex algebraic geometry states that, for any smooth projective variety, the Gauss map is finite; in particular, a smooth variety and its Gauss image have the same dimension (with the obvious exception of a linear space). Furthermore, even when the variety is not smooth, Zak proved a lower bound on the dimension of its Gauss image in terms of the dimension of its singul...

We study the Gauss map and the dual variety of a real-analytic immersion of a connected compact real-analytic manifold into a sphere or into a hyperbolic space. The dual variety is defined to be the set of all normal directions of the immersion. First, we show that the image of the Gauss map characterizes the manifold. Also we show that the dual variety characterizes the manifold. Besides, dual...

Following are the abstracts of contributions (i.e., talks and posters) to the 13th Annual Meeting of the IMS held at the National University of Ireland Maynooth, 6–8 September 2000. The abbreviations after the names designate: ‘M’ for main speaker, ‘S’ for speaker, ‘RS’ for research student, and ‘P’ for poster. The abstracts are included as provided by the contributors for this volume of the Bu...

To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the differential of the Gauss map of the underlying surface. The Gauss map assigns to each point in the surface the unit normal vector of the tangent plane to the surface...