Geometric structures on solutions of equations of adiabatic gas motion
- Authors: Yumaguzhin V.1
-
Affiliations:
- Program Systems Institute
- Issue: Vol 37, No 1 (2016)
- Pages: 87-100
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197352
- DOI: https://doi.org/10.1134/S1995080216010108
- ID: 197352
Cite item
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.
About the authors
V. Yumaguzhin
Program Systems Institute
Author for correspondence.
Email: yuma@diffiety.botik.ru
Russian Federation, Pereslavl’-Zalesskiy, 152020