The notion of principal configuration of immersions of surfaces into R3, due to Sotomayor and Gutierrez [16] for lines of curvature and umbilics, is extended to that of mean directional configuration for immersed surfaces in R4. This configuration consists on the families of mean directionally curved lines, along which the second fundamental form points in the direction of the mean curvature vector, and their singularities, called here H-singularities.
@article{urn:eudml:doc:41478,
title = {Mean directionally curved lines on surfaces immersed in R4.},
journal = {Publicacions Matem\`atiques},
volume = {47},
year = {2003},
pages = {415-440},
zbl = {1069.53006},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41478}
}
Mello, Luis Fernando. Mean directionally curved lines on surfaces immersed in R4.. Publicacions Matemàtiques, Tome 47 (2003) pp. 415-440. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41478/