Nonlinear Connections and Semisprays on Tangent Manifolds
نویسنده
چکیده
The well–known notions from tangent bundle geometry, like nonlinear connections and semisprays, are extended to bundle–type tangent manifolds. Also, new objects interesting from a dynamical point of view, like symmetries of nonlinear connections, are introduced. AMS Mathematics Subject Classification (2000): 58A30, 34A26, 37C10, 53C15
منابع مشابه
Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations
We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan–Kähler theorem. We consider a linear partial differential operator P given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that P is involutive and there is only one obst...
متن کاملBi–Hamiltonian Structures and Solitons
Methods in Riemann–Finsler geometry are applied to investigate bi–Hamiltonian structures and related mKdV hierarchies of soliton equations derived geometrically from regular Lagrangians and flows of non–stretching curves in tangent bundles. The total space geometry and nonholonomic flows of curves are defined by Lagrangian semisprays inducing canonical nonlinear connections (N–connections), Sas...
متن کاملA Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملNonholonomic Ricci Flows: III. Curve Flows and Solitonic Hierarchies
The geometric constructions are performed on (semi) Riemannian manifolds and vector bundles provided with nonintegrable distributions defining nonlinear connection structures induced canonically by metric tensors. Such spaces are called nonholonomic manifolds and described by two equivalent linear connections also induced unique forms by a metric tensor (the Levi Civita and the canonical distin...
متن کاملGravity as a Nonholonomic Almost Kähler
A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004