Politeknik Dergisi 2147-9429 Gazi Üniversitesi 10.2339/politeknik.670333 Engineering Mühendislik Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space https://orcid.org/0000-0003-3264-6239 Güler Erhan BARTIN ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜ 06 01 2021 24 2 517 520 01 04 2020 04 21 2020 Copyright © 1998, Politeknik Dergisi 1998 Politeknik Dergisi

In this study, rotational hypersurfaces in the 4-dimensional Euclidean space are discussed. Some relations of curvatures of hypersurfaces are given, such as the mean, Gaussian, and their minimality and flatness. In addition, Laplace-Beltrami operator has been defined for 4-dimensional hypersurfaces depending on the first fundamental form. Moreover, it is shown that each element of the 4×4 order matrix A, which satisfies the condition ∆^I R=AR, is zero, that is, the rotational hypersurface R is minimal.

In this study, rotational hypersurfaces in the 4-dimensional Euclidean space are discussed. Some relations of curvatures of hypersurfaces are given, such as the mean, Gaussian, and their minimality and flatness. In addition, Laplace-Beltrami operator has been defined for 4-dimensional hypersurfaces depending on the first fundamental form. Moreover, it is shown that each element of the 4×4 order matrix A, which satisfies the condition ∆^I R=AR, is zero, that is, the rotational hypersurface R is minimal.

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