Hypersphere and the Third Laplace-Beltrami Operator

Year 2022, , 727 - 732, 30.06.2022

Erhan Güler

https://doi.org/10.17798/bitlisfen.1109645

Abstract

In this work, we examine the differential geometric objects of the hypersphere h in four dimensional Euclidean geometry E^4. Giving some notions of four dimension, we consider the ith curvature formulas of the hypersurfaces of E^4. In addition, we reveal the hypersphere satisfying ∆^III h=Ah for some 4×4 matrix A.

Keywords

Euclidean space, Third Laplace-Beltrami operator, Hypersphere, Gauss map, Curvature

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