Jet Bundles as Whitney Sums


Kadıoğlu H.

2nd International E-Conference on Mathematical and Statistical Sciences: A Selçuk Meeting, Ankara, Turkey, 5 - 07 June 2023, pp.119

  • Publication Type: Conference Paper / Summary Text
  • City: Ankara
  • Country: Turkey
  • Page Numbers: pp.119
  • Yıldız Technical University Affiliated: Yes

Abstract

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.