Geodesic
On the characteristic curves on a surface in R^4
Journal of Singularities, Tome 22 (2020), pp. 28-39

Voir la notice de l'article provenant de la source Journal of Singularities website

We study some robust features of characteristic curves on smooth surfaces in R^4. These curves are analogous to the asymptotic curves in the elliptic region. A P_3(c)-point is an isolated special point at which the unique characteristic (or asymptotic) direction is tangent to the parabolic curve. At this point, by considering the cross-ratio invariant, we show that the 2-jet of the curve formed by the inflections of the characteristic curves is projectively invariant. In addition, we exhibit the possible configurations of the characteristic curves at a P_3(c)-point.
DOI : 10.5427/jsing.2020.22c
Classification : :57R45, 53A05, 53A20, 34A09, :34A09, 37C10 
@article{10_5427_jsing_2020_22c,
     author = {Jorge Luiz Deolindo-Silva},
     title = {On the characteristic curves on a surface in {R^4}},
     journal = {Journal of Singularities},
     pages = {28--39},
     publisher = {mathdoc},
     volume = {22},
     year = {2020},
     doi = {10.5427/jsing.2020.22c},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22c/}
}
TY  - JOUR
AU  - Jorge Luiz Deolindo-Silva
TI  - On the characteristic curves on a surface in R^4
JO  - Journal of Singularities
PY  - 2020
SP  - 28
EP  - 39
VL  - 22
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22c/
DO  - 10.5427/jsing.2020.22c
ID  - 10_5427_jsing_2020_22c
ER  - 
%0 Journal Article
%A Jorge Luiz Deolindo-Silva
%T On the characteristic curves on a surface in R^4
%J Journal of Singularities
%D 2020
%P 28-39
%V 22
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22c/
%R 10.5427/jsing.2020.22c
%F 10_5427_jsing_2020_22c
Jorge Luiz Deolindo-Silva. On the characteristic curves on a surface in R^4. Journal of Singularities, Tome 22 (2020), pp. 28-39. doi: 10.5427/jsing.2020.22c

Cité par Sources :