In this paper, by the studying of the Gauss map, Laplacian operator, curvatures of surfaces in R 1 and Bour’s theorem, we are going to identify surfaces of revolution with pointwise 1-type Gauss map property in 3−dimensional Minkowski space. Introduction The classification of submanifolds in Euclidean and Non-Euclidean spaces is one of the interesting topics in differential geometry and in this...

— We associate to any convenient nondegenerate Laurent polynomial f on the complex torus (C∗ )n a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its u...

We study Gauss maps of order k, associated to a projective variety X embedded in projective space via a line bundle L. We show that if X is a smooth, complete complex variety and L is a k-jet spanned line bundle on X , with k > 1, then the Gauss map of order k has finite fibers, unless X = Pn is embedded by the Veronese embedding of order k. In the case where X is a toric variety, we give a com...

The problem of counting lattice points on a hyperboloid of two sheets is Gauss’ circle problem in hyperbolic geometry. The problem of counting lattice points on a hyperboloid of one sheet does not have the same geometric interpretation, and in general, the solution(s) to Gauss’ circle problem gives a lower bound, but not an upper bound. In this paper, we describe an exception. Given an ample he...

The Shor algorithm [1] to factor numbers and its NMRimplementation [2] have propelled the field of quantum computation [3]. Recently a different factorization scheme [4] taking advantage of the periodicity properties of Gauss sums [5] has been proposed [6] and verified by two NMR-experiments [7, 8] and one experiment based on short laser pulses [9]. In the present paper we report the first impl...

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...

While Bayesian methods can significantly improve the quality of tomographic reconstructions, they require the solution of large iterative optimization problems. Recent results indicate that the convergence of these optimization problems can be improved by using sequential pixel updates, or Gauss-Seidel iterations. However, Gauss-Seidel iterations may be perceived as less useful when parallel co...

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...

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...