Canonical involution on double jet bundles


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KADIOĞLU H.

TURKISH JOURNAL OF MATHEMATICS, vol.41, no.4, pp.854-872, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.3906/mat-1511-82
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.854-872

Abstract

In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by primary and secondary structures belong to the same atlas. We prove that double jet bundles can be considered as a quotient of second order jet bundle. We show that there exists a natural involution that interchanges between primary and secondary vector bundle structures on double jet bundles.