The natural operators $T^{(0,0)} ⇝ T^{(1,1)}T^{(r)}$

• Autorzy: Włodzimierz M. Mikulski
• Języki publikacji: EN

Abstrakty

EN

We study the problem of how a map f:M → ℝ on an n-manifold M induces canonically an affinor $A(f): TT^{(r)}M → TT^{(r)}M$ on the vector r-tangent bundle $T^{(r)}M = (J^r(M,ℝ)₀)*$ over M. This problem is reflected in the concept of natural operators $A:T^{(0,0)}_{|ℳ fₙ} ⇝ T^{(1,1)}T^{(r)}$. For integers r ≥ 1 and n ≥ 2 we prove that the space of all such operators is a free (r+1)²-dimensional module over $𝓒^{∞}(T^{(r)}ℝ)$ and we construct explicitly a basis of this module.

Kategorie tematyczne

• 58A20: Jets
• 53A55: Differential invariants (local theory), geometric objects

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 96
• Numer: 1
• Strony: 5-16

Daty

wydano

2003

Twórcy

autor

Włodzimierz M. Mikulski

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/cm96-1-2