Hypersphere and the fourth Laplace-Beltrami operator in 4-space

Erhan Güler

doi:10.26637/mjm1101/001

Abstract

We consider hypersphere $\mathbf{x}(u,v,w)$ in the four dimensional Euclidean space ${\mathbb{E}}^{4}$. We compute the fourth Laplace-Beltrami operator the hypersphere satisfying $\Delta ^{IV}\mathbf{x=}\mathcal{A} \mathbf{x}$, where $\mathcal{A}\in Mat\left( 4,4\right)$.

Keywords:

Four space, Euclidean space, the fourth Laplace-Beltrami operator, hypersphere, Gauss map, curvatures

Mathematics Subject Classification:

53A07, 53C42

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Erhan Güler Faculty of Sciences, Department of Mathematics, Bartın University, 74100 Bartın, Turkey.

Pages: 1-10
Date Published: 01-01-2023
Vol. 11 No. 01 (2023): Malaya Journal of Matematik (MJM)

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