TY - JOUR
AU - Carrión Riveros, Carlos
AU - Vásquez Corro, Armando
PY - 2017/07/13
Y2 - 2024/08/07
TI - Laplace invariants in hypersurfaces parametrized by lines of curvature
JF - Selecciones Matemáticas
JA - Sel.Mat.
VL - 4
IS - 01
SE -
DO - 10.17268/sel.mat.2017.01.04
UR - https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1422
SP - 30-37
AB - In this work, using the Laplace invariants theory we give other proof for the following result: A proper Dupin hypersurfaces Mn for n ≥ 4 in Rn+1 with n distinct principal curvatures and<br />constant mobius curvature, cannot be parametrized by lines of curvature. Also, we study special classes of hypersurfaces Mn; n ≥ 3; in Rn+1, parametrized by lines of curvature with n distinct principal curvatures and we obtain a geometric relation when the Laplace invariants are vanish, we show that the foliations of Mn are umbilical hypersurfaces if and only if mijk = 0. Moreover, the foliations of Mn are Dupin hypersurfaces if and only if mij = 0.
ER -