Basic Classes of Timelike General Rotational Surfaces in the Four-dimensional Minkowski Space

TL;DR

This paper classifies and analyzes various geometric properties of timelike general rotational surfaces in four-dimensional Minkowski space, including flatness, mean curvature, and minimality, extending classical Euclidean results to a Lorentzian setting.

Contribution

It introduces a detailed study of timelike general rotational surfaces in Minkowski space, providing explicit descriptions of their geometric classes and special surface types.

Findings

Characterization of flat timelike rotational surfaces

Explicit descriptions of minimal surfaces in this class

Identification of surfaces with constant mean curvature

Abstract

In the present paper, we consider timelike general rotational surfaces in the Minkowski 4-space which are analogous to the general rotational surfaces in the Euclidean 4-space introduced by C. Moore. We study two types of such surfaces (with timelike and spacelike meridian curve, respectively) and describe analytically some of their basic geometric classes: flat timelike general rotational surfaces, timelike general rotational surfaces with flat normal connection, and timelike general rotational surfaces with non-zero constant mean curvature. We give explicitly all minimal timelike general rotational surfaces and all timelike general rotational surfaces with parallel normalized mean curvature vector field.