Generalized rotation surfaces in E4 with density

Abstract

In the present paper, we obtain the weighted mean and weighted Gaussian curvatures of a generalized rotation surface in E4 with density eλ1x2+λ2y2+λ3z2+λ4t2, where λi, i∈{1,2,3,4}, are not all zero and we give some results about weighted minimal and weighted flat generalized rotation surface in E4 with density eλ(x2+y2)+μ(z2+t2), where λ and μ are not all zero. Also, we obtain the weighted mean and weighted Gaussian curvatures of Klein bottle, Banchoff surface, Vranceanu rotation surface, and Clifford torus, which are examples of generalized rotation surfaces, in E4 with density eλ(x2+y2)+μ(z2+t2) and give some results for their minimality and flatness. © 2023 Elsevier B.V.