Calibrated geodesic foliations of hyperbolic space

YAMILE GODOY; MARCOS SALVAI

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2016 vol. 144 p. 359 - 367

0002-9939

Let $H$ be the hyperbolic space of dimension $n+1$. A geodesic foliation of $% H$ is given by a smooth unit vector field on $H$ all of whose integral curves are geodesics. Each geodesic foliation of $H$ determines an $n$% -dimensional submanifold $mathcal{M}$ of the $2n$-dimensional manifold $% mathcal{L}$ of all the oriented geodesics of $H$ (up to orientation preserving reparametrizations). The space $mathcal{L}$ has a canonical split semi-Riemannian metric induced by the Killing form of the isometry group of $H$. Using a split special Lagrangian calibration, we study the volume maximization problem for a certain class of geometrically distinguished geodesic foliations, whose corresponding submanifolds of $% mathcal{L}$ are space-like.