arXiv subjects

J. Basto-Gonçalves

Publications and source records attributed to J. Basto-Gonçalves.

2 recordsLinked to original sources

arXiv2013

Inflection points and asymptotic lines on Lagrangean surfaces

We describe the structure of the asymptotic lines near an inflection point of a Lagrangean surface, proving that in the generic situation it corresponds to two of the three possible cases when the discriminant curve has a cusp singularity. Besides being stable in general, inflection points are proved to exist on a compact Lagrangean surface whenever its Euler characteristic does not vanish.

math.DG↗

arXiv2013

Local geometry of surfaces in $\mathbf R^4$

The indicatrix or curvature ellipse and the characteristic curve of a surface in $\mathbf R^4$ are presented, as well as the projective duality connecting them. The characterisation of points in the surfaces as elliptic, parabolic and hyperbolic points, and the inflection points, are also discussed.

math.DG↗