# New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space

@inproceedings{Aquino2015NewCO, title={New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space}, author={C{\'i}cero P. Aquino and Henrique F. de Lima}, year={2015} }

- Published 2015
DOI:10.5817/am2015-4-201

In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space $\mathbb{H}^{n+1}$, that is, complete hypersurfaces of $\mathbb{H}^{n+1}$ whose mean curvature $H$ and normalized scalar curvature $R$ satisfy $R=aH+b$ for some $a$, $b\in \mathbb{R}$. In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 15 REFERENCES

## Some function-theoretic properties of complete Riemannian manifolds and their applications to geomet

VIEW 13 EXCERPTS

HIGHLY INFLUENTIAL

## Hypersurfaces with constant scalar curvature

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Hypersurfaces with parallel Ricci tensor

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## LINEAR WEINGARTEN HYPERSURFACES IN A UNIT SPHERE

VIEW 1 EXCERPT

## Global rigidity theorems of hypersurfaces

VIEW 1 EXCERPT

## Hypersurfaces With Constant Mean Curvature in Spheres

VIEW 1 EXCERPT