Geometric structures on solutions of equations of adiabatic gas motion

Abstract

In this paper we show that characteristic covectors of equations of n-dimensional adiabatic gas motion, n = 1, 2, 3, generate a geometric structure on every their solution. This structure consists of a hyperplane and a non degenerate cone in each cotangent space to a solution so that the hyperplane and the cone intersect only at the zero point. We investigate differential invariants of this structure. In particular, we find a natural linear connection on every solution. A torsion tensor of this connection is trivial for n = 1. For n = 2, 3, this tensor is not trivial in general. For n = 1, we calculate solutions having the linear connection with zero curvature tensor. For n = 2, 3, we calculate solutions with zero torsion tensor.