Hypersphere and the Third Laplace-Beltrami Operator

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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