Foliations of the hyperbolic space H³ by minimal surfaces
DOI:
https://doi.org/10.5902/2179460X90697Keywords:
Minimal surfaces, Hyperbolic space, FoliationAbstract
In this work, we present two foliations of the hyperbolic space by minimal surfaces. In each of these foliations, the leaves are invariant under the flux of a Killing field. In the first, the Killing field is of parabolic type, and in the second is of hyperbolic type.
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Barbosa, J. L. M., Gomes, J. d. M., & Silveira, A. M. (1987). Foliation of 3-dimensional space forms by surfaces with constant mean curvature. Bulletin of the Brazilian Mathematical Society, 18(2):1–12.
Carmo, M. P. d. & Dajczer, M. (1983). Rotation hypersurfaces in spaces of constant curvature. Transactions American Mathematical Society, 277(2):685–709.
Fornari, S. & Ripoll, J. B. (2004). Killing fields, mean curvature, translation maps. Illinois Journal of Mathematics, 48(4):1385–1403.
Meeks, W. H. (1988). The topology and geometry of embedded surfaces of constant mean curvature. Journal Differential Geometry, 27(3):539–552.
Sampaio, J. E. & Silva, E. C. d. (2024). Cmc foliations on euclidean spaces are minimal foliations. ArXiv, pages 1–22. https://arxiv.org/pdf/2404.13772.
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