Geometric structures on solutions of equations of 3-dimensional adiabatic gas motion

JOURNAL OF GEOMETRY AND PHYSICS

卷:85

Article

Yumaguzhin, Valeriy

关键词: System of equation of 3-dimensional adiabatic gas motion;    Explicit solution;    Jet-bundle;    Geometric structure;    Differential invariant;   

DOI  :  10.1016/j.geomphys.2014.05.002

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free