Surfaces in Minkowski 3-space on which H and K are linearly related
The paper is a study of surfaces in \(M^ 3\), a Minkowski 3-space, whose mean curvature H and extrinsic curvature K satisfy a non-trivial linear relationship \(\alpha +\beta H+\gamma K\equiv 0\), where \(\alpha\), \(\beta\), \(\gamma\) are constants. As an example of the results given in the paper we state the following: A spacelike or timelike surface in \(M^ 3\) on which \(\alpha +\beta H+\gamma K\equiv 0\), with \(\beta^ 2\neq 4\alpha \gamma\), is equidistant from at least one surface with H or K constant. This is an extension of the classical theorem of Bonnet, which associates an equidistant surface of constant \(K>0\) (resp. \(H\neq 0)\) to a surface of constant \(H\neq 0\) (resp. \(K>0)\).
scientific article; zbMATH DE number 3881434