Linearization of nonlinear connections on vector and affine bundles, and some applications

A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be applied after homogenization and restriction. Several applications in Classical Mechanics are provided

Meeting Minutes

Meeting regarding Academic Council charter revision and sabbaticals

On special types of nonholonomic 33-jets

summary:We deduce a classification of all special types of nonholonomic $3$-jets. In the introductory part, we summarize the basic properties of nonholonomic $r$-jets

Prolongation of pairs of connections into connections on vertical bundles

summary:Let $F$ be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the $F$-vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to $F$-vertical bundles. We also present some examples and applications

Contact elements on fibered manifolds

summary:For every product preserving bundle functor $T^\mu$ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_{k,l}^{r,s,q} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu$. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T(K_{k,l}^{r,s,q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_{k,l}^{r,s,q} Y$