Canonical involution on double jet bundles

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KADIOĞLU H.

TURKISH JOURNAL OF MATHEMATICS, cilt.41, sa.4, ss.854-872, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/mat-1511-82
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.854-872
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.