Abstract
In this paper, we show that characteristic covectors of a system of equations of 3-dimensional adiabatic gas motion generate a geometric structure on every solution of this system. This structure consists of a hyperplane and a non degenerate cone in every cotangent space to a solution. These hyperplane and cone intersect in zero point only. We construct differential invariants of this structure: a vector field, a conformal structure, a Lorentzian metric, and a linear connection. In the case of polytropic gas motion, we calculate classes of explicit solutions possessing the linear connection with zero torsion.
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