2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113842In this paper we study some properties of surfaces immersed in $\mathbf R ^4$ whose asymptotic lines are orthogonal. We also analyze necessary and sufficient conditions for the hypersphericity of surfaces in $\mathbf R ^4$.19 pagesDynamical SystemsDifferential Geometry53A05; 58C25Orthogonal Asymptotic Lines on Surfaces Immersed in $\mathbf R ^4$text