Akademik Veri Yönetim Sistemi
2nd International E-Conference on Mathematical and Statistical Sciences: A Selçuk Meeting, Ankara, Türkiye, 5 - 07 Haziran 2023, ss.119, (Özet Bildiri)
Jet bundles are mathematical tools that have many applications in fields such as partial differential equations, mechanics, singularity theory, and variational calculus.
In addition, they have a significant role in differential geometry, where they can be used to define the tangent bundle of higher order, such as the tangent bundle of p-k velocities. There are different ways of defining jet bundles, including using an equivalence relation between local sections of a given bundle, using an equivalence relation between curves on an arbitrary manifold, or using an equivalence relation on functions from R^p to M. This paper focuses on the latter type of jets, and it reviews necessary preliminary information on jet bundles and their properties, provides the geometric structure of the Whitney sum ⊕_p(TM), and defines a vector space structure on each fiber of the jet bundle. The paper also demonstrates that the jet bundle can be written as a Whitney sum of p-tangent bundles and that this representation allows for the definition of a Riemannian metric on the jet bundle.