Geometry of conic connections

Abstract: A conestructure 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 a joint work with Andreas Cap.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.