# Meridian Surfaces with Parallel Normalized Mean Curvature Vector Field in Pseudo-Euclidean 4-space with Neutral Metric

@article{Bulca2016MeridianSW, title={Meridian Surfaces with Parallel Normalized Mean Curvature Vector Field in Pseudo-Euclidean 4-space with Neutral Metric}, author={Bet{\"u}l Bulca and Velichka Milousheva}, journal={arXiv: Differential Geometry}, year={2016} }

We construct a special class of Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with timelike or spacelike axis and call them meridian surfaces. We give the complete classification of the meridian surfaces with parallel mean curvature vector field. We also classify the meridian surfaces with parallel normalized mean curvature vector. We show that in the family of the meridian surfaces there exist…

## 2 Citations

### Meridian Surfaces on Rotational Hypersurfaces with Lightlike Axis in ${\mathbb E}^4_2$

- Mathematics
- 2017

We construct a special class of Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with lightlike axis and…

### Meridian Surfaces on Rotational Hypersurfaces with Lightlike Axis in E 42

- Mathematics
- 2017

We construct a special class of Lorentz surfaces in the pseudoEuclidean 4-space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with lightlike axis and…

## 19 References

### Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-Space with Neutral Metric

- Mathematics
- 2016

In the present paper we consider a special class of Lorentz surfaces in the four-dimensional pseudo-Euclidean space with neutral metric which are one-parameter systems of meridians of rotational…

### COMPLETE CLASSIFICATION OF LORENTZ SURFACES WITH PARALLEL MEAN CURVATURE VECTOR IN ARBITRARY PSEUDO-EUCLIDEAN SPACE

- Mathematics
- 2010

Surfaces with parallel mean curvature vector play important roles in the theory of harmonic maps, differential geometry as well as in physics. Surfaces with parallel mean curvature vector in…

### Meridian Surfaces of Elliptic or Hyperbolic Type in the Four-dimensional Minkowski Space

- Mathematics
- 2014

We consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. We call these…

### Classification of spatial surfaces with parallel mean curvature vector in pseudo-Euclidean spaces of arbitrary dimension

- Mathematics
- 2009

Spatial surfaces with parallel mean curvature vector play some important roles in general relativity, theory of harmonic maps, as well as in differential geometry. Recently, spatial surfaces in…

### Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

- Mathematics
- 2009

Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with…

### Surfaces with parallel normalized mean curvature vector

- Mathematics
- 1980

A surfaceM in a Riemannian manifold is said to have parallel normalized mean curvature vector if the mean curvature vector is nonzero and the unit vector in the direction of the mean curvature vector…

### Special Classes of Meridian Surfaces in the Four-dimensional Euclidean Space

- Mathematics
- 2014

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of…

### Meridian Surfaces of Elliptic or Hyperbolic Type with Pointwise 1-type Gauss Map in Minkowski 4-Space

- Mathematics
- 2014

In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike…

### Submanifolds with parallel mean curvature vector in Riemannian and indefinite space forms

- Mathematics
- 2013

A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with…