Mikołaj Rotkiewicz

Bundle-theoretic methods for higher-order variational calculus

I will present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle $(E, \sigma, M)$. A bundle $\tilde{T}^{r,r} E\to T^{2r} M$ of higher semi-holonomic velocities of $\sigma$ will be constructed and an interesting canonical vector bundle morphism $\Upsilon_{k,\sigma}: \tilde{T}^{r,r} E\to E$ will be derived. Based on a joint paper with Micha\l\ J\'{o}\'{z}wikowski.