Classification of rotational surfaces in Euclidean space satisfying a linear relation between their principal curvatures

Rafael López, Álvaro Pámpano

We classify all rotational surfaces in Euclidean space whose principal curvatures ${\kappa }_1$ and ${\kappa }_2$ satisfy the linear relation ${\kappa }_1=a{\kappa }_2+b$, where $a$ and $b$ are two constants. We…