A Representation of the 1st-Order Variational Sequence in Field Theory

Jana Kašparová (Krpcová)

E-mail: Jana.Kasparova@math.slu.cz

Abstract. Variational sequence of order $r$ introduced by Krupka is defined on the $r$-jet prolongation of a fibered manifold $\pi :Y\rightarrow X$, as a quotient sequence of the de Rham sequence of sheaves. In this paper we describe explicitly the elements of the 1st-order variational sequence over an $n$-dimensional manifold $X$.

AMSclassification. 58E99, 58A12, 58A15, 58A20

Keywords. Fibered manifold, contact form, strongly contact form, trace decomposition problem, $q$-equation, sheaf, variational sequence