In:
Journal of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 103, No. 1 ( 2017-08), p. 45-58
Abstract:
In 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. Furthermore, working with different warped product models for $\mathbb{H}^{n+1}$ and supposing that certain natural inequalities involving two consecutive higher order mean curvature functions are satisfied, we study the rigidity and the nonexistence of complete hypersurfaces immersed in $\mathbb{H}^{n+1}$ .
Type of Medium:
Online Resource
ISSN:
1446-7887
,
1446-8107
DOI:
10.1017/S1446788716000549
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2017
detail.hit.zdb_id:
1478743-X
SSG:
17,1
