@article{Carrión Riveros_Vásquez Corro_2017, title={Laplace invariants in hypersurfaces parametrized by lines of curvature}, volume={4}, url={https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1422}, DOI={10.17268/sel.mat.2017.01.04}, abstractNote={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.}, number={01}, journal={Selecciones Matemáticas}, author={Carrión Riveros, Carlos and Vásquez Corro, Armando}, year={2017}, month={Jul.}, pages={30-37} }