Kazan, AhmetAltin, MustafaYoon, Dae Won2026-06-192026-06-1920230393-04401879-1662https://doi.org/10.1016/j.geomphys.2023.104770https://hdl.handle.net/20.500.12899/5865In the present paper, we obtain the weighted mean and weighted Gaussian curvatures of a generalized rotation surface in E4 with density e lambda 1x2+lambda 2y2+lambda 3z2+lambda 4t2, where lambda i, i is an element of {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 e lambda(x2+y2)+mu(z2+t2), where lambda and mu 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 e lambda(x2+y2)+mu(z2+t2) and give some results for their minimality and flatness.(c) 2023 Elsevier B.V. All rights reserved.eninfo:eu-repo/semantics/closedAccessGeneralized Rotation SurfaceDensityWeighted Mean CurvatureWeighted Gaussian CurvatureArticle10.1016/j.geomphys.2023.1047701862-s2.0-85147695259Q1WOS:000953410000001Q1