RIGHT CONOID HYPERSURFACES IN FOUR-SPACE

Erhan Güler, Mustafa Yıldız

DOI Number
https://doi.org/10.22190/FUMI230624053G
First page
817
Last page
828

Abstract


The right conoid hypersurfaces in the four-dimensional Euclidean space $\mathbb{E}^{4}$ are introduced. The matrices corresponding to the fundamental form, Gauss map, and shape operator of these hypersurfaces are calculated. By utilizing the Cayley--Hamilton theorem, the curvatures of these specific hypersurfaces are determined. Furthermore, the conditions for minimality are presented. Additionally, the Laplace--Beltrami operator of this family is computed, and some examples are provided.

Keywords

conoid hypersurfaces, Cayley--Hamilton theorem, four-dimensional space.

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References


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DOI: https://doi.org/10.22190/FUMI230624053G

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