Differential geometrical relations for a class of formal series

Alexandr Baranovitch

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...

The natural operators lifting $k$ -projectable vector fields to product-preserving bundle functors on $k$ -fibered manifolds.

Mikulski, Włodzimierz M., Tomáš, Jiři M. (2003)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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More morphisms between bundle gerbes.

Waldorf, Konrad (2007)

Theory and Applications of Categories [electronic only]

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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.

Horizontal forms on jet bundles.

Saunders, D.J. (2010)

Balkan Journal of Geometry and its Applications (BJGA)

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On lifts of some projectable vector fields associated to a product preserving gauge bundle functor on vector bundles

A. Ntyam, G. F. Wankap Nono, Bitjong Ndombol (2014)

Archivum Mathematicum

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For a product preserving gauge bundle functor on vector bundles, we present some lifts of smooth functions that are constant or linear on fibers, and some lifts of projectable vector fields that are vector bundle morphisms.

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 T²₁TM and TT²₁M

Miroslav Doupovec (1991)

Annales Polonici Mathematici

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

Some geometric aspects of the calculus of variations in several independent variables

David Saunders (2010)

Communications in Mathematics

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This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.