Surfaces of three-dimensional homogeneous plane waves
Giovanni Calvaruso, Lorenzo Pellegrino · Journal of Geometry and Physics · 2025
We investigate the geometry of surfaces in three-dimensional homogeneous non-symmetric plane waves. In particular, we obtain the full classification and explicit description of their totally geodesic and parallel examples and prove the nonexistence of proper totally umbilical surfaces. Moreover, we characterize their minimal surfaces, providing some explicit examples.