Honam Mathematical Journal (호남수학학술지)

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ROTATIONAL HYPERSURFACES CONSTRUCTED BY DOUBLE ROTATION IN FIVE DIMENSIONAL EUCLIDEAN SPACE 𝔼5

  • Erhan Guler (Department of Mathematics, Faculty of Sciences, Bartin University, Kutlubey Campus)
  • Received : 2023.02.15
  • Accepted : 2023.08.23
  • Published : 2023.12.20
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Abstract

We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space 𝔼5. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curvatures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal Δx=𝓐x, where 𝓐 is the 5 × 5 matrix in 𝔼5.

Keywords

References

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