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pro vyhledávání: '"Craizer, Marcos"'
The higher order contact of a quadric with a surface in $3$-space at a non-degenerate point is obtained by the Moutard quadric in the Darboux direction. In this paper, we discuss the extension of this result to hypersurfaces in arbitrary dimensions.<
Externí odkaz:
http://arxiv.org/abs/2401.12712
Autor:
Craizer, Marcos
A smooth affine minimal surface with indefinite metric can be obtained from a pair of smooth non-intersecting spatial curves by Lelieuvre's formulas. These surfaces may present singularities, which are generically cuspidal edges and swallowtails. By
Externí odkaz:
http://arxiv.org/abs/2401.06540
In this paper we define the class of constant affine mean curvature (CAMC) discrete asymptotic nets, which contains the well-known classes of affine spheres and affine minimal asymptotic nets. This class is defined by considering fields of compatible
Externí odkaz:
http://arxiv.org/abs/2212.14868
We consider in this paper discrete improper affine spheres based on asymptotic nets. In this context, we distinguish the discrete edges and vertices that must be considered singular. The singular edges can be considered as discrete cuspidal edges, wh
Externí odkaz:
http://arxiv.org/abs/2211.00442
We prove a discrete analog of a certain four-vertex theorem for space curves. The smooth case goes back to the work of Beniamino Segre and states that a closed and smooth curve whose tangent indicatrix has no self-intersections admits at least four p
Externí odkaz:
http://arxiv.org/abs/2208.04454
A bisection line divides a convex planar curve into two parts with equal areas. It is natural to study the envelope of these lines, which in general present singularities. The polygonal case is particularly inte\-resting, since there are several diff
Externí odkaz:
http://arxiv.org/abs/2203.10559
Autor:
Craizer, Marcos, Garcia, Ronaldo Alves
Line congruences are $2$-dimensional families of lines in $3$-space. The singularities that appear in generic line congruences are folds, cusps and swallowtails. In this paper we give a geometric description of these singularities. The main tool used
Externí odkaz:
http://arxiv.org/abs/2108.06525
The classical isoperimetric inequality can be extended to a general normed plane. In the Euclidean plane, the defect in the isoperimetric inequality can be calculated in terms of the signed areas of some singular sets. In this paper we consider norme
Externí odkaz:
http://arxiv.org/abs/2008.12801
Autor:
Craizer, Marcos, Garcia, Ronaldo A.
In this paper we discuss the behavior of the curvature lines of a transversal eq\"uiaffine vector field along a surface in $3$-space at isolated umbilical points.
Comment: 12 pages. This article was originally part of earlier versions of arXiv:
Comment: 12 pages. This article was originally part of earlier versions of arXiv:
Externí odkaz:
http://arxiv.org/abs/2008.04765
Publikováno v:
Advances in Mathematics 374 (2020) 107326 [open access]
Given a Lagrangian submanifold $L$ of the affine symplectic $2n$-space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension $2n$, both of whose sets of singularities contain $L$. Although these imp
Externí odkaz:
http://arxiv.org/abs/1906.03127