We show that covariant field theory for sections of Ï€ : E â†’ M lifts in a natural way to the bundle of vertically adapted linear frames LÏ€E. Our analysis is based on the fact that LÏ€E is a principalâ€¦ (More)

The Poisson and graded Poisson Schouten-Nijenhuis algebras of symmetric and anti-symmetric contravariant tensor fields, respectively, on an n-dimensional manifold M are shown to be n-symplectic. Thisâ€¦ (More)

This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulationsâ€¦ (More)

We present preliminary results for a prequantization procedure that leads in a natural way to the Dirac equation. The starting point is the recently introduced n-symplectic geometry on the bundle ofâ€¦ (More)

Most of the previous shape-based human activity models are built with either a linear assumption or an extrinsic interpretation of the nonlinear geometry of the shape space, both of which proved toâ€¦ (More)

We identify the fiber-bundle-with-connection structure that underlies the Lanczos H-tensor formulation of Riemannian geometrical structure. Motivated by the Lanczos Lagrangian that includes theâ€¦ (More)

This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulationsâ€¦ (More)

High dimensional data exhibits distinct properties compared to its low dimensional counterpart, which causes a common performance decrease and a formidable computational cost increase of traditionalâ€¦ (More)