Curvature properties of the slowness surface of the system of crystal acoustics for cubic crystals

Abstract

In this paper we study geometric properties of the slowness surface of the system of crystal acoustics for cubic crystals. In particular we shall study curvature properties of the surface and the behaviour of the surface near singular points. The main result is that in the generic nearly isotropic case there are no planes which are tangent to the surface along entire curves. This is in contrast with what happens for the slowness surface of the system of crystal optics for bi-axial crystals. Geometric information of the type we shall obtain is needed to understand the long-time behaviour of global solutions of the system of crystal acoustics.