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

Abstract

In this paper, we investigate rotational hypersurfaces family in n-dimensional Euclidean space En. Our focus is on studying the Gauss map Gof this family with respect to the operator Lk, which acts on functions defined on the hypersurfaces. The operator Lk 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 Ln-3 to the Gauss map G, we establish a classification theorem. This theorem establishes a connection between the n x n matrix A, and the Gauss map Gthrough the equation Ln-3G=AG. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar