Family of Totally Umbilical Hypersurfaces in an Einstein Space

1943 ◽  
Vol 44 (2) ◽  
pp. 271 ◽  
Author(s):  
Yung-Chow Wong
Keyword(s):  
Einstein Space ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

scholarly journals Some Results on Super Quasi-Einstein Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Shyamal Kumar Hui ◽  
Richard S. Lemence
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifolds ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces

This paper deals with the study of super quasi-Einstein manifolds admitting -curvature tensor. The totally umbilical hypersurfaces of are also studied. Among others, the existence of such a manifold is ensured by a nontrivial example.

ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE

2016 ◽  
Vol 103 (1) ◽  
pp. 45-58
Author(s):  
C. P. AQUINO ◽  
M. BATISTA ◽  
H. F. DE LIMA
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Warped Product ◽  
Gauss Map ◽  
Higher Order ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces ◽  
Product Models ◽  
Higher Order Mean Curvature ◽  
Complete Hypersurfaces

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$\mathbb{H}^{n+1}$.

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