Displaying similar documents to “Differential geometrical relations for a class of formal series”

Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.

Wlodzimierz M. Mikulski (2006)

Extracta Mathematicae

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Let A be a Weil algebra and V be an A-module with dim V < ∞. Let E → M be a vector bundle and let TE → TM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form Tφ : T E → ΛT*TM ⊗ TTE on TE → TM from a linear semibasic tangent valued p-form φ : E → ΛT*M ⊗­ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[Tφ, Tψ]] = T ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and ψ on E → M. We apply...

On curves and jets of curves on supermanifolds

Andrew James Bruce (2014)

Archivum Mathematicum

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In this paper we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we make a quick comparison with the notion of a curve presented here are other common notions found in the literature.

Natural transformations of higher order cotangent bundle functors

Jan Kurek (1993)

Annales Polonici Mathematici

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We determine all natural transformations of the rth order cotangent bundle functor T r * into T s * in the following cases: r = s, r < s, r > s. We deduce that all natural transformations of T r * into itself form an r-parameter family linearly generated by the pth power transformations with p =1,...,r.

Natural transformations between T²₁T*M and T*T²₁M

Miroslav Doupovec (1991)

Annales Polonici Mathematici

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We determine all natural transformations T²₁T*→ T*T²₁ where T k r M = J 0 r ( k , M ) . We also give a geometric characterization of the canonical isomorphism ψ₂ defined by Cantrijn et al.