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 ℝ3. 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.
Cite this article
Yoshiyasu Yasutomi, Modiﬁed Elastic Wave Equations on Riemannian and Kähler Manifolds. Publ. Res. Inst. Math. Sci. 43 (2007), no. 2, pp. 471–504DOI 10.2977/PRIMS/1201011792