2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219797Let $S$ be a Riemann surface of analytic finite type or the unit disk in the complex plane. Let $[μ]$ denote the Teichmüller equivalence classes of Beltrami differentials $μ$. We apply the Fundamental Inequalities to obtain a binary infinitesimal form of Teichmüller metric. Using this form, we define "\emph{angle}" between two geodesics originating from a point and conjecture that the sum of the angles of a triangle in $T(S)$ should be less than $π$ if $S$ is of analytic finite type. As a consequence, the well-known necessary condition for two geodesics coinciding is derived immediately.10 pages(to appear after modified)Complex Variables32G15, 30C75, 30C62text