Rotational hypersurfaces family satisfying L_n−3G=AG in the n-dimensional Euclidean space

In this paper, we investigate rotational hypersurfaces family in n-dimensional Euclidean space Eⁿ. Our focus is on studying the Gauss map G of this family with respect to the operator L_k, which acts on functions defined on the hypersurfaces. The operator L_k can be viewed as a modified Laplacian and is known by various names, including the Cheng–Yau operator in certain cases. Specifically, we focus on the scenario where k=n−3 and n≥3. By applying the operator L_n−3 to the Gauss map G, we establish a classification theorem. This theorem establishes a connection between the n×n matrix A, and the Gauss map G through the equation L_n−3G=AG.