A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show that the space of smooth sections of such distributions need not be finitely ...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family...

In this article, we give numerical restrictions on the Chern classes of Ulrich bundles higher-dimensional manifolds, which are inspired by results Casnati in case surfaces. As a by-product, prove that only projective manifolds whose tangent bundle is twisted cubic and Veronese surface. Moreover, cotangent never Ulrich.

We consider how to test for group differences of shapes given longitudinal data. In particular, we are interested in differences of longitudinal models of each group's subjects. We introduce a generalization of principal geodesic analysis to the tangent bundle of a shape space. This allows the estimation of the variance and principal directions of the distribution of trajectories that summarize...

We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle in the α corrections is an instanton. For heterotic compactifications in dimension six this fixes the choice of that connection to be the unique SU(3) instanton on a stab...