On norms and subsets of linear spaces
In this paper a Weil approach to quasijets is discussed. For given manifolds and , a quasijet with source and target is a mapping which is a vector homomorphism for each one of the vector bundle structures of the iterated tangent bundle [A. Dekrét, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by the bundle of quasijets from to ; the space of non-holonomic -jets from to is embeded into . On the other hand, the bundle of -quasivelocities...
Let () denote the Grassmann manifold of linear -spaces (resp. oriented -spaces) in , and suppose . As an easy consequence of the Steenrod obstruction theory, one sees that -fold Whitney sum of the nontrivial line bundle over always has a nowhere vanishing section. The author deals with the following question: What is the least () such that the vector bundle admits a nowhere vanishing section ? Obviously, , and for the special case in which , it is known that . Using results...
This paper has two parts. Part one is mainly intended as a general introduction to the problem of sectioning vector bundles (in particular tangent bundles of smooth manifolds) by everywhere linearly independent sections, giving a survey of some ideas, methods and results.Part two then records some recent progress in sectioning tangent bundles of several families of specific manifolds.