Zero mean curvature submanifolds as generalizations of rotational surfaces in Minkowski space
Streszczenie
Catenoids are rotationally symmetric hypersurfaces with zero mean curvature in Minkowski space. This paper considers three generalizations of catenoids. First, we construct a generalization by replacing the rotational orbits of catenoids with minimal submanifolds within these orbits. Second, we present another generalization: $O(m)\times O_1(n)$-invariant hypersurfaces in $\mathbb {L}^{m+n+2}$ with zero mean curvature, where $O_1(n)$ is the group of Lorentz transformations, and we classify all profile curves. Finally, we consider two types of birotationally symmetric functions. These functions are the sum of two functions, each depending on a radial variable, and their graphs have zero mean curvature. If the graph is not a hyperplane, one of the functions is linear, while the other represents a catenoid of the corresponding dimension under rotation.
