Hypersphere and the Third Laplace-Beltrami Operator

Authors : Erhan GÜLER

Pages : 727-732

Doi:10.17798/bitlisfen.1109645

View : 16 | Download : 13

Publication Date : 2022-06-30

Article Type : Research Paper

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