Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations
| Autor: | T. Bayrakdar, Z. Ok Bayrakdar |
|---|---|
| Přispěvatelé: | Ege Üniversitesi |
| Rok vydání: | 2018 |
| Předmět: |
Computer Science::Machine Learning
Article Subject Differential equation QC1-999 General Physics and Astronomy Riemannian geometry Computer Science::Digital Libraries 01 natural sciences Statistics::Machine Learning symbols.namesake 0103 physical sciences 0101 mathematics Metric connection Mathematics Physics Applied Mathematics 010102 general mathematics Jet bundle Mathematical analysis Submanifold Ordinary differential equation Computer Science::Mathematical Software symbols Vector field Mathematics::Differential Geometry 010307 mathematical physics Scalar curvature |
| Zdroj: | Advances in Mathematical Physics, Vol 2018 (2018) |
| ISSN: | 1687-9139 1687-9120 |
| DOI: | 10.1155/2018/7590847 |
| Popis: | WOS: 000425432000001 We construct metric connection associated with a first-order differential equation by means of the generator set of a Pfaffian system on a submanifold of an appropriate first-order jet bundle. We firstly show that the inviscid and viscous Burgers' equations describe surfaces attached to an ODE of the form dx/dt = u(t,x) with certain Gaussian curvatures. In the case of PDEs, we show that the scalar curvature of a three-dimensional manifold encoding a system of first-order PDEs is determined in terms of the integrability condition and the Gaussian curvatures of the surfaces corresponding to the integral curves of the vector fields which are annihilated by the contact form. We see that an integral manifold of any PDE defines intrinsically flat and totally geodesic submanifold. |
| Databáze: | OpenAIRE |
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