On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space
- Autores: Nikos Georgiou
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 111, Nº 2, 2012, págs. 187-209
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15224
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Resumen
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
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