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ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE
Journal of the Australian Mathematical Society, 2016In this paper, we establish new characterization results concerning totally umbilical hypersurfaces of the hyperbolic space$\mathbb{H}^{n+1}$, under suitable constraints on the behavior of the Lorentzian Gauss map of complete hypersurfaces having some constant higher order mean curvature.
Aquino, C. P. +2 more
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Busemann Spaces and Hyperbolic Spaces
2014A Busemann space (also known as a Busemann convex space) is a geodesic metric space X such that for any two geodesics \(\gamma: \left [a,b\right ] \rightarrow X\) and \(\gamma ^{{\prime}}: \left [a^{{\prime}},b^{{\prime}}\right ] \rightarrow X,\) the map \(D_{\gamma,\gamma ^{{\prime}}}: \left [a,b\right ] \times \left [a^{{\prime}},b^{{\prime}}\right ]
William Kirk, Naseer Shahzad
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The Problem of Plateau in Hyperbolic Space
American Journal of Mathematics, 1942Not ...
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Bethe lattices in hyperbolic space
Physical Review E, 1993A recently suggested geometrical embedding of Bethe-type lattices (branched polymers) in the hyperbolic plane [R. Mosseri and J. F. Sadoc, J. Phys. Lett. 43, L249 (1982); J. A. de Miranda-Neto and F. Moraes, J. Phys. I. France 2, 1657 (1992)] is shown to be only a special case of a whole continuum of possible realizations that preserve some of the ...
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Harmonic Spinors on Hyperbolic Space
Canadian Mathematical Bulletin, 1993AbstractThe purpose for this short note is to describe the space of harmonic spinors on hyperbolicn-spaceHn. This is a natural continuation of the study of harmonic functions onHnin [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms onHnwere ...
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The moduli space of the modular group in complex hyperbolic geometry
Inventiones Mathematicae, 2003John Parker +2 more
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