Foliated geometric structures, and leafwise completeness

SEMINARIO DE JÓVENES INVESTIGADORES

Conferenciante: Lilia Mehidi (Universidad de Granada)

Abstract: We explore the notion of tangential \((G,X)\)-foliations, which can be understood as foliations with a \((G,X)\)-structure on the leaves that varies continuously from a leaf to another. The general question in this context is how the topology of the manifold influences the geometry of the leaves. Although there is some old literature on this topic, it seems that none have addressed the completeness of such structures along the leaves.

In this talk, we will see how these foliations naturally occur, through examples in pseudo-Riemannian geometry. I will then discuss some related questions, with a particular focus on the completeness issue, and present some applications.