Institut de recherche mathématique avancée

Résumé : A cone structure on a complex manifold $M$ is given by a closed submanifold $\mathcal C\subset \mathbb P TM$ of the projectived tangent bundle of $M$ which is submersive over $M$. Such geometric structures arise naturally in differential and algebraic geometry and, when they do, they are often equipped with a conic connection which specifies a distinguished family of curves on $M$ in directions of $\mathcal C$. A classical example is the null cone bundle of a holomorphic conformal structure equipped with the conic connection induced by the null-geodesics. In a joint work with Jun-Muk Hwang we defined an important local invariant for so-called characteristic conic connections, namely the cubic torsion. In this talk I will give a geometric interpretation of the cubic torsion and will discuss some applications. This talk is based on joint work in progress with Andreas \v Cap.