The Geometry of Higher-Order Hamilton Spaces

Fedosov quantization of Lagrange–Finsler and Hamilton–Cartan spaces and Einstein gravity lifts on (co) tangent bundles

“…In this section, we outline some results from the geometry of LagrangeFinsler [33,34] and Hamilton-Cartan [31,32] spaces.…”

“…In brief, such distinguished (by N-connection) components are called respectively d-objects, d-field (for some physical fields of tensor, spinor nature ...), d-tensors, d-vectors, d-forms, d-connections etc, see details in Refs. [31,32,33,34,38,29]. Proposition 2.1 There are canonical frame structures (local N-adapted (co-)bases ) defined by canonical N-connections:…”

“…The natural step in this direction is to apply the methods of the geometry of Hamilton and Cartan spaces and generalizations [31,32] (such spaces are respectively dual to the Lagrange and Finsler spaces and generalizations [33,34]). …”

Models of Finseler Spaces With Given Geodesics

“…Following idea Moor introduced, in a three-dimensional Finsler space, the intrinsic field of orthonormal frame which consists of the normalized supporting element , the normalized torsion vector and a unit vector orthogonal to them and developed a theory of three-dimensional Finsler spaces. Generalizing the Berwald's and Moor's ideas, Miron andMatsumoto[ (1986), (1977), (1989)] developed a theory of intrinsic orthonormal frame fields on n-dimensional Finsler space as follows. 2) = 2) 2 , where, 2 is the length of 2) relative to .…”

Graded bundles and homogeneity structures

“…Note also that double homogeneity structures, unlike double vector bundle structures, generate a new homogeneity structure h defined by h t = h 1 t • h 2 t . There are, of course, natural questions concerning the concepts of duality for homogeneity structures and their applications in physics, investigated recently by Tulczyjew [13] in the context of the higher tangent bundles (see also [8]), which we decided, however, to postpone to a separate paper.…”