TY  - JOUR
T1  - Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space
TT  - Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space
AU  - Güler, Erhan
PY  - 2021
DA  - June
DO  - 10.2339/politeknik.670333
JF  - Politeknik Dergisi
PB  - Gazi Üniversitesi
WT  - DergiPark
SN  - 2147-9429
SP  - 517
EP  - 520
VL  - 24
IS  - 2
LA  - en
AB  - 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.
KW  - 4-dimensional Euclidean space
KW  - Laplace-Beltrami operator
KW  - rotational hypersurface
KW  - curvature
N2  - 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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UR  - https://doi.org/10.2339/politeknik.670333
L1  - https://dergipark.org.tr/tr/download/article-file/1067185
ER  -