On lifting of connections to Weil bundles

• Autorzy: Jan Kurek , Włodzimierz M. Mikulski
• Języki publikacji: EN

Abstrakty

EN

We prove that the problem of finding all $ℳ f_m$-natural operators $B:Q⟿ QT^A$ lifting classical linear connections ∇ on m-manifolds M to classical linear connections $B_M(∇)$ on the Weil bundle $T^{A}M$ corresponding to a p-dimensional (over ℝ) Weil algebra A is equivalent to the one of finding all $ℳ f_m$-natural operators $C:Q ⟿ (T¹_{p-1},T* ⊗ T* ⊗ T)$ transforming classical linear connections ∇ on m-manifolds M into base-preserving fibred maps $C_M(∇):T¹_{p-1}M = ⨁^{p-1}_{M} TM → T*M ⊗ T*M ⊗ TM$.

Kategorie tematyczne

• 58A32: Natural bundles
• 58A20: Jets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 103
• Numer: 3
• Strony: 319-324

Daty

wydano

2012

Twórcy

autor

Jan Kurek

• Institute of Mathematics, Maria Curie-Skłodowska University, Pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

autor

Włodzimierz M. Mikulski

• Chair of Geometry, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ap103-3-7