  Elastic wave propagation is a century-old problem. Unlike on a flat manifold,
analytical solution is not well established for a curved manifold. In this
study we take a step towards building an analytical framework for solving the
elastic wave propagation problem on an arbitrary manifold which admits a
Riemannian metric with a global non-zero scalar curvature. We demonstrate the
accuracy of the method by solving for some test cases, and also discuss some
interesting physical insight that comes from solving the wave equations for
non-vanishing curvature.
