It is hereby established that, in Euclidean spaces of finite dimension, bounded self-contracted curves have finite length. This extends the main result of Daniilidis et al. (J. Math. Pures Appl. 94:183–199, 2010) concerning ...

We say that a germ of vector field X in (...) is tangent to a holomorphic foliation defined by a germ of integrable 1-form (...). In this thesis we aim to study some geometric properties arising from this setting. We first ...

This work is divided int two parts. In the first part of the work, in Theorem 2.1, we give a first version of Botts fórmula for a compact complex orbifold with isolated singularities. In Theorem 2.4, using a good resolution ...

This thesis is dedicated to the study of conditions to ensure the existence of formal separatrices for a foliation defined by a germ of real analytical vector field with an algebraically isolated singularity at the origin ...

We extend the Induced Matter Theory of gravity (IMT) to 5D curved spacetimes by using the Weitzenböck representation of connections on a 5D curved spacetime. In this representation the 5D curvature tensor becomes null, so ...