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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 3-manifolds by Harris & Paternain '13, is that
positive Ricci curvature tends to yield contact forms, namely, 1-forms 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 3-manifold: 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 4-manifold, 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.
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