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## trenRotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean SpaceRotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space

#### Erhan GÜLER [1]

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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Primary Language en Engineering Research Article Orcid: 0000-0003-3264-6239Author: Erhan GÜLER (Primary Author)Institution: BARTIN ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜCountry: Turkey Application Date : January 4, 2020 Publication Date : June 1, 2021
 Bibtex @research article { politeknik670333, journal = {Politeknik Dergisi}, issn = {}, eissn = {2147-9429}, address = {Gazi Üniversitesi Teknoloji Fakültesi 06500 Teknikokullar - ANKARA}, publisher = {Gazi University}, year = {2021}, volume = {24}, pages = {517 - 520}, doi = {10.2339/politeknik.670333}, title = {Rotational Hypersurfaces Satisfying ∆\^I R=AR in the Four-Dimensional Euclidean Space}, key = {cite}, author = {Güler, Erhan} } APA Güler, E . (2021). Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space . Politeknik Dergisi , 24 (2) , 517-520 . DOI: 10.2339/politeknik.670333 MLA Güler, E . "Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space" . Politeknik Dergisi 24 (2021 ): 517-520 Chicago Güler, E . "Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space". Politeknik Dergisi 24 (2021 ): 517-520 RIS TY - JOUR T1 - Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space AU - Erhan Güler Y1 - 2021 PY - 2021 N1 - doi: 10.2339/politeknik.670333 DO - 10.2339/politeknik.670333 T2 - Politeknik Dergisi JF - Journal JO - JOR SP - 517 EP - 520 VL - 24 IS - 2 SN - -2147-9429 M3 - doi: 10.2339/politeknik.670333 UR - https://doi.org/10.2339/politeknik.670333 Y2 - 2020 ER - EndNote %0 Politeknik Dergisi Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space %A Erhan Güler %T Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space %D 2021 %J Politeknik Dergisi %P -2147-9429 %V 24 %N 2 %R doi: 10.2339/politeknik.670333 %U 10.2339/politeknik.670333 ISNAD Güler, Erhan . "Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space". Politeknik Dergisi 24 / 2 (June 2021): 517-520 . https://doi.org/10.2339/politeknik.670333 AMA Güler E . Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space. Politeknik Dergisi. 2021; 24(2): 517-520. Vancouver Güler E . Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space. Politeknik Dergisi. 2021; 24(2): 517-520. IEEE E. Güler , "Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space", Politeknik Dergisi, vol. 24, no. 2, pp. 517-520, Jun. 2021, doi:10.2339/politeknik.670333

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