On Factorable Surfaces of Finite Chen Type in the Lorentz–Heisenberg Space H3

This paper is about a problem at the intersection of differential geometry, spectral analysis and the theory of manifolds. The study of finite-type subvarieties was initiated by Chen in the 1970s, with the aim of obtaining improved estimates for the mean total curvature of compact subvarieties in Euclidean space. The concept of a finite-type subvariety naturally extends that of a minimal subvariety or surface, the latter being closely related to variational calculus. In this work, we classify factorable surfaces in the Lorentz–Heisenberg space H3, equipped with a flat metric satisfying ΔIri=λiri, which satisfies algebraic equations involving coordinate functions and the Laplacian operator with respect to the surface’s first fundamental form.