As was shown by a part of the authors, for a given (2, 3, 5)-distribution D on a 5-dimensional manifold Y , there is, locally, a Lagrangian cone structure C on another 5-dimensional manifold X which consists of abnormal or singular paths of (Y, D). We give a characterization of the class of Lagrangian cone structures corresponding to (2, 3, 5)-distributions. Thus we complete the duality between (2, 3, 5)-distributions and Lagrangian cone structures via pseudo-product structures of type G 2 . A local example of non-flat perturbations of the global model of flat Lagrangian cone structure which corresponds to (2, 3, 5)-distributions is given.

No abstract

We consider bundle homomorphisms between tangent distributions and vector bundles of the same rank. We study the conditions for fundamental singularities when the bundle homomorphism is induced from a Morin map. When the tangent distribution is the contact structure, we characterize singularities of the bundle homomorphism by using the Hamilton vector fields.(Saji)

No abstract

No abstract