
Geometry, Topology, and Physics Seminar, Spring 2015
Part of the NSF/UCSB ‘Research Training Group’ in Topology and Geometry
Organizers:
Dave Morrison and
Zhenghan Wang.
Meets 4:00  5:30 p.m. on selected Fridays in South Hall 6635.
Other Quarters: [
Fall, 2021;
Winter, 2020;
Fall, 2019;
Spring, 2018;
Winter, 2018;
Fall, 2017;
Spring, 2017;
Wnter, 2017;
Fall, 2016;
Spring, 2016;
Winter, 2016;
Fall, 2015;
Spring, 2015;
Winter, 2014;
Fall, 2013;
Fall, 2012;
Fall, 2011;
Winter, 2011;
Spring, 2010;
Winter, 2010;
Fall, 2009;
Spring, 2009;
Winter, 2009;
Fall, 2008;
Spring, 2008;
Winter, 2008;
Fall, 2007;
Spring, 2007;
Winter, 2007;
Fall, 2006
]
May. 15 
Amir Aazami (Kavli IPMU, Univ. of Tokyo)
Abstract:
We investigate timelike and null vector flows on closed Lorentzian
manifolds and their relationship to Ricci curvature. The guiding observation, first
observed for closed Riemannian 3manifolds by Harris & Paternain '13, is that
positive Ricci curvature tends to yield contact forms, namely, 1forms metrically
equivalent to unit vector fields with geodesic flow. We carry this line of thought
over to the Lorentzian setting. First, we observe that the same is true on a closed
Lorentzian 3manifold: if X is a global timelike unit vector field with geodesic
flow satisfying Ric(X,X) > 0, then g(X,•) is a contact form with Reeb vector field X,
at least one of whose integral curves is closed. Second, we show that on a closed
Lorentzian 4manifold, if X is a global null vector field satisfying \nabla_XX = X and
Ric(X) > divX  1, then dg(X,•) is a symplectic form and X is a Liouville vector field.


