Seminar talk, 25 February 2015

Speaker: Valery Yumaguzhin

Title: Differential invariants on solutions of equations of adiabatic gas motion

Abstract:
The talk will discuss the system of equations of adiabatic gas motion in $n$-dimensional space, $n=1,2,3$.

Characteristic covectors of this system 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 metric, and a linear connection with torsion in general position.

In the case of polytropic gas motion, we calculate classes of explicit solutions possessing the linear connection with zero torsion.

Video
Slides: Yumaguzhin V. Differential invariants on solutions of equations of adiabatic gas motion (presentation at the Krasil'shchik's IUM Seminar, 25 February 2015).pdf