Surfaces of Revolution with Constant Mean Curvature in Galilean 3-Space

Revolution surfaces with zero mean curvature in the Galilean 3-space have been extensively studied in the literature. However, revolution surfaces with non-zero constant mean curvature in this geometric setting have not yet been investigated in a systematic way. In this paper, we address this gap by studying surfaces of revolution in the Galilean 3-space with constant mean curvature. We derive the necessary and sufficient differential conditions for such surfaces and obtain explicit parametrizations of the corresponding families. The results extend the theory beyond the minimal case and reveal geometric features that arise from the degenerate nature of the Galilean metric. Several examples are presented to illustrate the obtained surfaces and to emphasize the qualitative differences between minimal and non-minimal constant mean curvature configurations.