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

Abstract

Abstract. In the present paper we consider a special class of Lorentz surfaces in the fourdimensional pseudo-Euclidean 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 minimal and quasi-minimal meridian surfaces. We also classify the meridian surfaces with non-zero constant mean curvature.

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

“…The same result holds true for meridian surfaces lying on rotational hypersurfaces with spacelike or timelike axis [4].…”

“…In the present paper, the new contribution to the theory of meridian surfaces is the construction of 2-dimensional Lorentz surfaces in the pseudo-Euclidean space E 4 2 which are one-parameter systems of meridians of a rotational hypersurface with lightlike axis. They are analogous to the meridian surfaces lying on rotational hypersurfaces with spacelike or timelike axis in E 4 2 which have been studied in [3] and [4]. We show that all meridian surfaces are surfaces with flat normal connection and classify completely the meridian surfaces with constant Gauss curvature (Theorem 4.1 and Theorem 4.2).…”

“…Following the idea from the Euclidean and Minkowski spaces, in [3] and [4] we constructed Lorentz meridian surfaces in the pseudo-Euclidean 4-space E 4 2 as one-parameter systems of meridians of rotational hypersurfaces with timelike or spacelike axis. We gave the classification of quasi-minimal meridian surfaces and meridian surfaces with constant mean curvature [3].…”

“…We gave the classification of quasi-minimal meridian surfaces and meridian surfaces with constant mean curvature [3]. The classification of meridian surfaces with parallel mean curvature vector field and the classification of meridian surfaces with parallel normalized mean curvature vector is given in [4].…”