Title: An introduction to surfaces embedded in sub-Riemannian manifolds
Speaker: Lucia Tessarolo
Abstract: Over the past 30 years, sub-Riemannian geometry has become an independent research field, with motivations from various mathematical domains. In this talk, we will introduce the notion of sub-Riemannian manifolds, with a particular focus on 3-dimensional contact sub-Riemannian manifolds. These consist of a smooth manifold M equipped with a distribution D(i.e. a sub-bundle of the tangent bundle) that satisfies some special properties.
We will then explore the geometry of a surface S embedded in such a manifold. Unlike in the Riemannian case, we will see that S does not inherit a sub-Riemannian structure. However, it does inherit certain geometric objects, such as a measure and a foliation F which corresponds to the restriction of D to S.. This foliation becomes singular at a special set of points, known as characteristic points.
To these points, we associate a curvature-like invariant that captures the local structure of the foliation. In the final part of the talk, we will dive into my research and we will see how this invariant is connected to specific properties of the intrinsic Laplacian on the surface.
We will then explore the geometry of a surface S embedded in such a manifold. Unlike in the Riemannian case, we will see that S does not inherit a sub-Riemannian structure. However, it does inherit certain geometric objects, such as a measure and a foliation F which corresponds to the restriction of D to S.. This foliation becomes singular at a special set of points, known as characteristic points.
To these points, we associate a curvature-like invariant that captures the local structure of the foliation. In the final part of the talk, we will dive into my research and we will see how this invariant is connected to specific properties of the intrinsic Laplacian on the surface.
Some snacks will be provided before and after the talk.