Event Details
Título: Variations for submanifolds in graded manifolds.
Impartida por: Gianmarco Giovannardi.
Fecha: 25 de febrero de 2021 de 12:00-13:00.
Resumen: The aim of this talk is to present the deformability properties of submanifolds immersed in graded manifolds that are a generalization of Carnot manifolds. We consider an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are admissible. It turns out that the associated variational vector fields must satisfy a system of partial differential equations of first order on the submanifold. Moreover, given a vector field solution of this system, we provide a sufficient condition that guarantees the possibility of deforming the original submanifold by variations preserving its degree. In the one-dimensional case, the integrability of compact supported vector fields depends on the surjection of the holonomy map at the endpoints. As in the case of singular curves in sub-Riemannian geometry, there are examples of isolated surfaces that cannot be deformed in any direction. This talk is based on my joint work with G. Citti and M. Ritoré.
Link de la reuníon: https://meet.google.com/yrc-wpte-dbj
Impartida por: Gianmarco Giovannardi.
Fecha: 25 de febrero de 2021 de 12:00-13:00.
Resumen: The aim of this talk is to present the deformability properties of submanifolds immersed in graded manifolds that are a generalization of Carnot manifolds. We consider an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are admissible. It turns out that the associated variational vector fields must satisfy a system of partial differential equations of first order on the submanifold. Moreover, given a vector field solution of this system, we provide a sufficient condition that guarantees the possibility of deforming the original submanifold by variations preserving its degree. In the one-dimensional case, the integrability of compact supported vector fields depends on the surjection of the holonomy map at the endpoints. As in the case of singular curves in sub-Riemannian geometry, there are examples of isolated surfaces that cannot be deformed in any direction. This talk is based on my joint work with G. Citti and M. Ritoré.
Link de la reuníon: https://meet.google.com/yrc-wpte-dbj
