Estás viendo actualmente el perfil de Amir B. Aazami. Vuelve al Historial para mostrar todas las conferencias o realiza una nueva búsqueda

Conferencias impartidas por Amir B. Aazami

The Newman-Penrose formalism for Riemannian 3-manifolds

Kavli IPMU (WPI), The University of Tokyo

We adapt the Newman-Penrose formalism in general relativity to the setting of three-dimensional Riemannian geometry, and prove the following results. Given a Riemannian 3-manifold without boundary and a smooth unit vector field \(X\) with geodesic flow, if an integral curve of \(X\) is hypersurface-orthogonal at a point, then it is so at every point along that curve. Furthermore, if \(X\) is complete, hypersurface-orthogonal, and satisfies \(Ric(X,X) \geq 0\), then the divergence of \(X\) must be nonnegative. As an app- lication, we show that when \(Ric > 0\), a geodesic and divergence-free unit vector field cannot be hypersurface-orthogonal; the case \(Ric < 0\) yields known results pertaining to unit length Killing vector fields. Along the way, we connect this formalism to some recent results from contact geometry, and mention how the Newman-Penrose formalism may be used to help classify scalar-flat Riemannian 3-manifolds.

Seminario 1ª Planta, IEMath-GR

Amir B. Aazami

Kavli IPMU (WPI), The University of Tokyo (Japón)

Conferencias impartidas
1
Visitas al departamento
2
Última visita
Página web personal

¿Los datos no son correctos? Por favor, contacta con nosotros para solucionarlo.