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

Authors

  • Nikos Georgiou

DOI:

https://doi.org/10.7146/math.scand.a-15224

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 γΣ 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.

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Published

2012-12-01

How to Cite

Georgiou, N. (2012). On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space. MATHEMATICA SCANDINAVICA, 111(2), 187–209. https://doi.org/10.7146/math.scand.a-15224

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Articles