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比利时vs摩洛哥足彩 ,
university of california san diego

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math 258 - differential geometry

amir babak aazami

contact and symplectic structures on closed lorentzian manifolds

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.

host: lei ni

may 14, 2015

1:00 pm

ap&m 5402

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