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In this paper is studied the relationship between quadratic tangencies of principal lines with the boundary of a surface and the Darbouxian umbilics of a smooth boundaryless surface which approximates it through the process of thickening and smoothing defined here. Neste trabalho são estudadas as linhas de curvaturas principais de uma superfície com bordo e da superfície regular, sem bordo, obtida pelo processo de engrossamento e regularização. É analisada a relação entre as tangências quadráticas das folheações principais com o bordo e os pontos umbílicos Darbouxianos, da superfície sem bordo, que bifurcam dos referidos pontos de tangências

Umbilic and Tangential Singularities on Configurations of Principal Curvature Lines