Modified Elastic Wave Equations on Riemannian and Kähler Manifolds

Abstract

We introduce some geometrically invariant systems of differential equations on any Riemannian manifolds and also on any Kähler manifolds, which are natural extena sions of the elastic wave equations on $R^3$. Further we prove the local decomposition theorems of distribution solutions for those systems. In particular, the solutions of our systems on Kähler manifolds are decomposed into 4 solutions with different propagation speeds.