Higher Order Tangent Bundles
نویسندگان
چکیده
منابع مشابه
Higher-order tangent and secant numbers
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The aim of the paper is to prove that T M , the tangent space of order k ≥ 1 of a manifold M , is diffeomorphic with T 1 k M , the tangent space of k–velocities, and also with ( T 1 k )∗ M , the cotangent space of k–covelocities, via suitable Lagrangians. One prove also that a hyperregular Lagrangian of first order on M can give rise to such diffeomorphisms. M.S.C. 2000: 53C60, 53C80, 70H50.
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Let M be a differentiable manifold. A vector field Γ of TM which corresponds to a system of second order ordinary differential equations on M is called a second order Hamiltonian vector field if it is the Hamiltonian field of a function F ∈ C∞(TM) with respect to a Poisson structure P of TM . We formulate the direct problem as that of finding Γ if P is given, and the inverse problem as that of ...
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ژورنال
عنوان ژورنال: Mediterranean Journal of Mathematics
سال: 2016
ISSN: 1660-5446,1660-5454
DOI: 10.1007/s00009-016-0812-7