Higher-order and Weil generalization of Grassmannian

Abstract

We give a simple mechanical motivation for a generalization of the classical Grassmannian considered as a space of m-dimensional linear subspaces of Rk to higher-orders cases. Our efforts are prolongated to the Weil functor theory, motivated by non-holonomic and semi-holonomic jets, applicable in the description of the Cosserat model.We give a simple mechanical motivation for a generalization of the classical Grassmannian considered as a space of m-dimensional linear subspaces of Rk to higher-orders cases. Our efforts are prolongated to the Weil functor theory, motivated by non-holonomic and semi-holonomic jets, applicable in the description of the Cosserat model.