Geometria Constant mean curvature surfaces in 3-manifolds admitting a Killing vector field Miguel Manzano
07-04-2016 - 15:45 AULA 211 (Largo San L. Murialdo,1) A Killing submersion is a Riemannian submersion from an
orientable 3-manifold to an orientable surface, such that the fibres of the
submersion are the integral curves of a Killing vector field without
zeroes. The interest of this family of structures is that it yields a
common treatment for a vast family of 3-manifolds, including, among others,
the simply-connected homogeneous ones and the warped products with
1-dimensional fibres. In the first part of this talk we will give existence and uniqueness
results for Killing submersions in terms of some geometric functions
defined on the base surface. In the second part, we will consider constant
mean curvature surfaces immersed in the total space of a Killing submersion
which are transversal to the Killing vector field. This will take us to the
classification of compact orientable stable surfaces with constant mean
curvature immersed in such 3-manifolds. Dropping the stability condition,
we will show that if the total space of a Killing submersion admits an
immersed minimal sphere then the base surface is also a sphere.
org: VIVIANI Filippo
|