Hi all. On any smooth surface one can use the metric to define
Christoffel symbols, define a covariant derivative, and a covariant
Laplacian which one can use to set up a wave equation. For no
particular reason it occurred to me that one might get interesting
solutions of the wave equation on the hyperbolic plane or in hyperbolic 3-space. A Google search didn't turn up anything. Does anyone know of
any relevant literature? I set up the wave equation for the unit disk
in the Poincare and Klein metrics, but in both cases I got a mess that
seems unsolvable (by humble me anyways). Any thoughts on this? Or
perhaps my idea that the problem is worth looking into was overly
optimistic?
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