The geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on TM. The metrizability of a given semispray is of special importance. In this paper, the metric associated with the semispray S is applied in order to study some types of foliations on the tangent bundle which are compatible with SODE structure. Indeed, suff...

We extend the scope of a former paper to vector bundle problems involving more than one vector bundle. As the main application, we obtain the solution of the well-known moduli problems of vector bundles associated with general quivers. Subject Classification: 14D20, 16G20.

We extend the scope of a former paper to vector bundle problems involving more than one vector bundle. As the main application, we obtain the solution of the well-known moduli problems of vector bundles associated with general quivers. Subject Classification: 114D20, 16G20.

Let X be a smooth projective curve over the field of complex numbers, and fix a homogeneous representation ρ : GL(r)−→ GL(V). Then, one can associate to every vector bundle E of rank r over X a vector bundle Eρ with fibre V . We would like to study triples (E,L,φ) where E is a vector bundle of rank r over X , L is a line bundle over X , and φ : Eρ −→ L is a non-trivial homomorphism. This set-up...