  In this paper, we investigate topological modes of different physical systems
defined on arbitrary two-dimensional curved surfaces. We consider the shallow
water equations, inhomogeneous Maxwell's equations, Jackiw-Rebbi model and show
how the topological protection mechanism responses to the presence of curvature
in different situations. We show the existence of a line gap in the considered
models and study the condition on the curve which can host topological modes.
