Calibrated geodesic foliations of hyperbolic space
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- by Yamile Godoy and Marcos Salvai PDF
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Abstract:
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 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.References
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Additional Information
- Yamile Godoy
- Affiliation: FaMAF - CIEM, Ciudad Universitaria, 5000 Córdoba, Argentina
- MR Author ID: 1043601
- Email: ygodoy@famaf.unc.edu.ar
- Marcos Salvai
- Affiliation: FaMAF - CIEM, Ciudad Universitaria, 5000 Córdoba, Argentina
- MR Author ID: 603972
- Email: salvai@famaf.unc.edu.ar
- Received by editor(s): November 28, 2014
- Published electronically: July 30, 2015
- Additional Notes: The authors were partially supported by CONICET, FONCyT, SECyT (UNC)
- Communicated by: Michael Wolf
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 359-367
- MSC (2010): Primary 53C38, 53C12, 53C22, 53C50
- DOI: https://doi.org/10.1090/proc/12834
- MathSciNet review: 3415602