A global characterization of jet bundles of \(p^ 1\)-velocities and covelocities (Q1903538)

The authors first give the notion of \(p\)-almost tangent structures on a smooth \((p + 1)n\)-dimensional manifold \(M\) and give the global characterization of the tangent bundle of \(p^1\)-velocities in terms of the integrability of \(p\)-almost tangent structures. Next, the authors give similar notions of \(p\)-almost cotangent bundles and the global characterization of cotangent bundles of \(p^1\)-covelocities. For the proofs the authors use the characterization of vector bundles by \textit{T. Nagano} [J. Differ. Geom. 2, 253-264 (1968; Zbl 0172.46903)].