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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Calibrated geodesic foliations of hyperbolic space
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by Yamile Godoy and Marcos Salvai PDF
Proc. Amer. Math. Soc. 144 (2016), 359-367 Request permission

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.
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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