On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space

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Abstract

We study area-stationary surfaces in the space L(H3) of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. We prove that every holomorphic curve in L(H3) is an area-stationary surface. We then classify Lagrangian area-stationary surfaces Σ in L(H3) and prove that the family of parallel surfaces in H3 orthogonal to the geodesics γ ∞ Σ form a family of equidistant tubes around a geodesic. Finally we find an example of a two parameter family of rotationally symmetric area-stationary surfaces that are neither Lagrangian nor holomorphic.

Original languageEnglish
Pages (from-to)187-209
Number of pages23
JournalMathematica Scandinavica
Volume111
Issue number2
DOIs
Publication statusPublished - 2012
Externally publishedYes

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