Natural transformations of higher order tangent bundles and jet spaces

Lagrangians and higher order tangent spaces

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.

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

a characterization of the infinitesimal conformal transformations on tangent bundles

Higher-Order Preconnections in Synthetic Differential Geometry of Jet Bundles

In our previous papers (Nishimura [2001 and 2003]) we dealt with jet bundles from a synthetic perch by regarding a 1-jet as something like a pinpointed (nonlinear) connection (called a preconnection) and then looking on higherorder jets as repeated 1-jets. In this paper we generalize our notion of preconnection to higher orders, which enables us to develop a non-repetitive but still synthetic a...

On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...