• Corpus ID: 237091105

On the geometry of non-degenerate surfaces in Lorentzian homogeneous $3$-manifolds

@inproceedings{Albujer2021OnTG,
  title={On the geometry of non-degenerate surfaces in Lorentzian homogeneous \$3\$-manifolds},
  author={Alma L. Albujer and F{\'a}bio R. dos Santos},
  year={2021}
}
In this paper we deal with non-degenerate surfaces Σ immersed in the 3dimensional homogeneous space L(κ, τ) endowed with two different metrics, the one induced by the Riemannian metric of E(κ, τ) and the non-degenerate metric inherited by the Lorentzian one of L(κ, τ). Therefore, we have two different geometries on Σ and we can compare them. In particular, we study the case where the mean curvature functions with respect to both metrics simultaneously vanish, and in this case we show that the… 

References

SHOWING 1-10 OF 14 REFERENCES

Isometric immersions into 3-dimensional homogeneous manifolds

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous Riemannian manifold with a 4-dimensional

Generalized Calabi correspondence and complete spacelike surfaces

We construct a twin correspondence between graphs with prescribed mean curvature in three-dimensional Riemannian Killing submersions and spacelike graphs with prescribed mean curvature in

A New Approach to Minimal and Maximal Hypersurfaces in Product Spaces

AbstractIn this paper we introduce a new method for the study of non-degenerate hypersurfaces immersed into product spaces of the form $$M^n\times \mathbb {R}$$Mn×R, with $$M^n$$Mn a Riemannian

Ruled minimal surfaces in the three-dimensional Heisenberg group

It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three dimensional Riemannian Heisenberg group. It is also shown that

Extensions of the duality between minimal surfaces and maximal surfaces

As a generalization of the classical duality between minimal graphs in E3 and maximal graphs in L3, we construct the duality between graphs of constant mean curvature H in Bianchi-Cartan-Vranceanu

Semi-Riemannian Geometry With Applications to Relativity

Manifold Theory. Tensors. Semi-Riemannian Manifolds. Semi-Riemannian Submanifolds. Riemannian and Lorenz Geometry. Special Relativity. Constructions. Symmetry and Constant Curvature. Isometries.

Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds

We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in

Complete constant mean curvature surfaces in homogeneous spaces

In this paper we classify complete surfaces of constant mean curvature whose Gaussian curvature does not change sign in a simply connected homogeneous manifold with a 4dimensional isometry group.