Related papers: Lagrange Geometries on Tangent Manifolds
For a manifold embedded in an inner product space, we express geometric quantities such as {\it Hamilton vector fields, affine and Levi-Civita connections, curvature} in global coordinates. Instead of coordinate indices, the global formulas…
This short and fairly informal note is an attempt to explain how methods of homological algebra may be brought to bear on problems in symplectic geometry. We do this by looking at a familiar sample question, which is that of the topology of…
Principal bundles have at least three different definitions, depending on the category of geometric objects studied. In Differential Geometry, they are defined as locally trivial projection map of smooth manifolds with an atlas whose…
Radu Miron's approach to modelling of generalized Lagrange, Finsler and Kaluza-Klein spaces on vector (super) bundles provided with compatible nonlinear and distinguished connections and metric structures is discussed in connection with the…
We give a Finsler non-linear connection by a new simplified definition for not only regular case but also singular case. In regular case, it corresponds to non-linear connection part of Berwald's connection, but our connection is expressed…
Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…
In this article, we review some aspects of gravitational field and cosmology based on Finsler and Finsler-like generalized metric structures. The geometrical framework of these spaces allows further investigation of locally-anisotropic…
Special coordinate systems are constructed in a neighborhood of a point or of a curve. Taylor expansions can then be easily inferred for the metric, the connection, or the Finsler Lagrangian in terms of curvature invariants. These…
A linear connection on a Finsler manifold is called compatible to the Finsler function if its parallel transports preserve the Finslerian length of tangent vectors. Generalized Berwald manifolds are Finsler manifolds equipped with a…
In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…
We define the tangent Euler top in General Relativity through a constrained Lagrangian on the orthonormal frame bundle. The corresponding motions are studied to various degrees of approximation, the lowest of which is shown to yield the…
We study geometry of the phase space for finite-dimensional dynamical systems with degenerate Lagrangians. The Lagrangian and Hamiltonian constraint formalisms are treated as different local-coordinate pictures of the same invariant…
In this paper I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, f, on the cotangent bundle of a differentiable manifold M. This will enable me to use the second vertical…
Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…
We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for…
Manifolds with a commutative and associative multiplication on the tangent bundle are called F-manifolds if a unit field exists and the multiplication satisfies a natural integrability condition. They are studied here. They are closely…
Our goal in this paper is to make an attempt to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. First, we introduce the notion of the…
Lorentz invariance is one of the foundations of modern physics; however, Lorentz violation may happen from the perspective of quantum gravity, and plenty of studies on Lorentz violation have arisen in recent years. As a good tool to explore…
In this paper, we construct a field theory unifying gravity and electromagnetism in the context of Extended Absolute Parallelism (EAP-) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…